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engineering
fluid mechanics
Fluid Mechanics Fundamentals And Applications 3rd Edition Yunus Cengel, John Cimbala - Solutions
Air at 2.50 kg/m3 enters a nozzle that has an inlet-to-exit area ratio of 2:1 with a velocity of 120 m/s and leaves with a velocity of 330 m/s. Determine the density of air at the exit.
The water level in a tank is 55 ft above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leading from the tank to the nozzle is a pump,
A pressurized 2-m-diameter tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level initially is 3 m above the outlet. The tank air pressure above the water level is maintained at 450 kPa absolute and the atmospheric pressure is 100 kPa.
The air in a 6-m × 5-m × 4-m hospital room is to be completely replaced by conditioned air every 20 min. If the average air velocity in the circular air duct leading to the room is not to exceed 5 m/s, determine the minimum diameter of the duct.
A D0 = 8-m-diameter tank is initially filled with water 2 m above the center of a D = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through a L = 80-m-long pipe connected to the valve. The friction factor of the pipe is given to be f = 0.015,
In some applications, elbow-type flow meters like the one shown in Fig. P5–115 are used to measure flow rates. The pipe radius is R, the radius of curvature of the elbow is λ, and the pressure difference ΔP across the curvature inside the pipe is measured. From the potential flow theory, it is
The cylindrical water tank with a valve at the bottom shown in Fig. P5–116 contains air at the top part at the local atmospheric pressure of 100 kPa and water as shown. Is it possible to completely empty this tank by fully opening the valve? If not, determine the water height in the tank when
A rigid tank of volume 1.5 m3 initially contains atmospheric air at 20°C and 150 kPa. Now a compressor is turned on, and atmospheric air at a constant rate of 0.05 m3/s is supplied to the tank. If the pressure and density in the tank varies as P/ρ1.4 = constant during charging, (a) Obtain a
Water flows in a 5-cm-diameter pipe at a velocity of 0.75 m/s. The mass flow rate of water in the pipe is(a) 353 kg/min (b) 75 kg/min (c) 37.5 kg/min(d) 1.47 kg/min (e) 88.4 kg/min
Air at 100 kPa and 20°C flows in a 12-cm-diameter pipe at a rate of 9.5 kg/min. The velocity of air in the pipe is(a) 1.4 m/s (b) 6.0 m/s (c) 9.5 m/s (d) 11.8 m/s(e) 14.0 m/s
A water tank initially contains 140 L of water. Now, equal rates of cold and hot water enter the tank for a period of 30 minutes while warm water is discharged from the tank at a rate of 25 L/min. The amount of water in the tank at the end of this 30-min period is 50 L. The rate of hot water
Water enters a 4-cm-diameter pipe at a velocity of 1 m/s. The diameter of the pipe is reduced to 3 cm at the exit. The velocity of the water at the exit is(a) 1.78 m/s (b) 1.25 m/s (c) 1 m/s (d) 0.75 m/s(e) 0.50 m/s
The pressure of water is increased from 100 kPa to 900 kPa by a pump. The mechanical energy increase of water is(a) 0.9 kJ/kg (b) 0.5 kJ/kg (c) 500 kJ/kg (d) 0.8 kJ/kg(e) 800 kJ/kg
A 75-m-high water body that is open to the atmosphere is available. Water is run through a turbine at a rate of 200 L/s at the bottom of the water body. The pressure difference across the turbine is(a) 736 kPa (b) 0.736 kPa (c) 1.47 kPa (d) 1470 kPa(e) 368 kPa
A pump is used to increase the pressure of water from 100 kPa to 900 kPa at a rate of 160 L/min. If the shaft power input to the pump is 3 kW, the efficiency of the pump is(a) 0.532 (b) 0.660 (c) 0.711 (d) 0.747 (e) 0.855
The motor of a pump consumes 1.05 hp of electricity. The pump increases the pressure of water from 120 kPa to 1100 kPa at a rate of 35 L/min. If the motor efficiency is 94 percent, the pump efficiency is(a) 0.75 (b) 0.78 (c) 0.82 (d) 0.85 (e) 0.88
Which parameter is not related in the Bernoulli equation?(a) Density (b) Velocity (c) Time (d) Pressure(e) Elevation
Consider incompressible, frictionless flow of a fluid in a horizontal piping. The pressure and velocity of a fluid is measured to be 150 kPa and 1.25 m/s at a specified point. The density of the fluid is 700 kg/m3. If the pressure is 140 kPa at another point, the velocity of the fluid at that point
Consider incompressible, frictionless flow of water in a vertical piping. The pressure is 240 kPa at 2 m from the ground level. The velocity of water does not change during this flow. The pressure at 15 m from the ground level is(a) 227 kPa (b) 174 kPa (c) 127 kPa (d) 120 kPa(e) 113 kPa
Consider water flow in a piping network. The pressure, velocity, and elevation at a specified point (point 1) of the flow are 150 kPa, 1.8 m/s, and 14 m. The pressure and velocity at point 2 are 165 kPa and 2.4 m/s. Neglecting frictional effects, the elevation at point 2 is(a) 12.4 m (b) 9.3
The static and stagnation pressures of a fluid in a pipe are measured by a piezometer and a pitot tube to be 200 kPa and 210 kPa, respectively. If the density of the fluid is 550 kg/m3, the velocity of the fluid is(a) 10 m/s (b) 6.03 m/s (c) 5.55 m/s (d) 3.67 m/s(e) 0.19 m/s
The static and stagnation pressures of a fluid in a pipe are measured by a piezometer and a pitot tube. The heights of the fluid in the piozemeter and pitot tube are measured to be 2.2 m and 2.0 m, respectively. If the density of the fluid is 5000 kg/m3, the velocity of the fluid in the pipe is(a)
The difference between the heights of energy grade line (EGL) and hydraulic grade line (HGL) is equal to(a) z (b) P/ρg (c) V2/2g (d ) z + P/ρg (e) z + V2/2g
Water at 120 kPa (gage) is flowing in a horizontal pipe at a velocity of 1.15 m/s. The pipe makes a 90° angle at the exit and the water exits the pipe vertically into the air. The maximum height the water jet can rise is(a) 6.9 m (b) 7.8 m (c) 9.4 m(d) 11.5 m (e) 12.3 m
Water is withdrawn at the bottom of a large tank open to the atmosphere. The water velocity is 6.6 m/s. The minimum height of the water in the tank is(a) 2.22 m (b) 3.04 m (c) 4.33 m (d) 5.75 m (e) 6.60 m
Water at 80 kPa (gage) enters a horizontal pipe at a velocity of 1.7 m/s. The pipe makes a 90° angle at the exit and the water exits the pipe vertically into the air. Take the correction factor to be 1. If the irreversible head loss between the inlet and exit of the pipe is 3 m, the height the
Seawater is to be pumped into a large tank at a rate of 165 kg/min. The tank is open to the atmosphere and the water enters the tank from a 80-m-height. The overall efficiency of the motor-pump unit is 75 percent and the motor consumes electricity at a rate of 3.2 kW. Take the correction factor to
Water enters a pump at 350 kPa at a rate of 1 kg/s. The water leaving the pump enters a turbine in which the pressure is reduced and electricity is produced. The shaft power input to the pump is 1 kW and the shaft power output from the turbine is 1 kW. Both the pump and turbine are 90 percent
An adiabatic pump is used to increase the pressure of water from 100 kPa to 500 kPa at a rate of 400 L/min. If the efficiency of the pump is 75 percent, the maximum temperature rise of the water across the pump is(a) 0.096°C (b) 0.058°C (c) 0.035°C (d) 1.52°C(e) 1.27°C
The shaft power from a 90 percent-efficient turbine is 500 kW. If the mass flow rate through the turbine is 575 kg/s, the extracted head removed from the fluid by the turbine is(a) 48.7 m (b) 57.5 m (c) 147 m (d) 139 m (e) 98.5 m
Using a large bucket whose volume is known and measuring the time it takes to fill the bucket with water from a garden hose, determine the mass flow rate and the average velocity of water through the hose.
Your company is setting up an experiment that involves the measurement of airflow rate in a duct, and you are to come up with proper instrumentation. Research the available techniques and devices for airflow rate measurement, discuss the advantages and disadvantages of each technique, and make a
Water of density ρ = 998.2 kg/m3 flows through a fireman’s nozzle—a converging section of pipe that accelerates the flow. The inlet diameter is d1 = 0.100 m, and the outlet diameter is d2 = 0.050 m. The average velocity, momentum flux correction factor, and gage pressure are known at the inlet
How is the angular momentum equation obtained from Reynolds transport equations?
Express the angular momentum equation in scalar form about a specified axis of rotation for a fixed control volume for steady and uniform flow.
Express the unsteady angular momentum equation in vector form for a control volume that has a constant moment of inertia I, no external moments applied, one outgoing uniform flow stream of velocity V(vector), and mass flow rate ṁ.
Consider two rigid bodies having the same mass and angular speed. Do you think these two bodies must have the same angular momentum? Explain.
Water is flowing through a 15-cm-diameter pipe that consists of a 3-m-long vertical and 2-m-long horizontal section with a 90° elbow at the exit to force the water to be discharged downward, as shown in Fig. P6–55, in the vertical direction. Water discharges to atmospheric air at a velocity of 7
A large lawn sprinkler with two identical arms is used to generate electric power by attaching a generator to its rotating head. Water enters the sprinkler from the base along the axis of rotation at a rate of 5 gal/s and leaves the nozzles in the tangential direction. The sprinkler rotates at a
Reconsider the lawn sprinkler in Prob. 6–56E. If the rotating head is somehow stuck, determine the moment acting on the head.Data from Problem 56A large lawn sprinkler with two identical arms is used to generate electric power by attaching a generator to its rotating head. Water enters the
The impeller of a centrifugal pump has inner and outer diameters of 13 and 30 cm, respectively, and a flow rate of 0.15 m3/s at a rotational speed of 1200 rpm. The blade width of the impeller is 8 cm at the inlet and 3.5 cm at the outlet. If water enters the impeller in the radial direction and
The impeller of a centrifugal blower has a radius of 18 cm and a blade width of 6.1 cm at the inlet, and a radius of 30 cm and a blade width of 3.4 cm at the outlet. The blower delivers atmospheric air at 20°C and 95 kPa. Disregarding any losses and assuming the tangential components of air
Water enters vertically and steadily at a rate of 35 L/s into the sprinkler shown in Fig. P6–60 with unequal arms and unequal discharge areas. The smaller jet has a discharge area of 3 cm2 and a normal distance of 50 cm from the axis of rotation. The larger jet has a discharge area of 5 cm2 and a
Repeat Prob. 6–60 for a water flow rate of 50 L/s.Data from Problem 60.Water enters vertically and steadily at a rate of 35 L/s into the sprinkler shown in Fig. P6–60 with unequal arms and unequal discharge areas. The smaller jet has a discharge area of 3 cm2 and a normal distance of 50 cm from
Consider a centrifugal blower that has a radius of 20 cm and a blade width of 8.2 cm at the impeller inlet, and a radius of 45 cm and a blade width of 5.6 cm at the outlet. The blower delivers air at a rate of 0.70 m3/s at a rotational speed of 700 rpm. Assuming the air to enter the impeller in the
Reconsider Prob. 6–62. For the specified flow rate, investigate the effect of discharge angle α2 on the minimum power input requirements. Assume the air to enter the impeller in the radial direction (α1 = 0°), and vary α2 from 0° to 85° in increments of 5°. Plot the variation of power
Water enters the impeller of a centrifugal pump radially at a rate of 45 cfm (cubic feet per minute) when the shaft is rotating at 500 rpm. The tangential component of absolute velocity of water at the exit of the 2-ft outer diameter impeller is 110 ft/s. Determine the torque applied to the
Pelton wheel turbines are commonly used in hydroelectric power plants to generate electric power. In these turbines, a high-speed jet at a velocity of Vj impinges on buckets, forcing the wheel to rotate. The buckets reverse the direction of the jet, and the jet leaves the bucket making an angle β
A lawn sprinkler with three identical arms is used to water a garden by rotating in a horizontal plane by the impulse caused by water flow. Water enters the sprinkler along the axis of rotation at a rate of 60 L/s and leaves the 1.5-cm-diameter nozzles in the tangential direction. The bearing
Water enters vertically and steadily at a rate of 10 L/s into the sprinkler shown in Fig. P6–71. Both water jets have a diameter of 1.2 cm. Disregarding any frictional effects, determine (a) The rotational speed of the sprinkler in rpm (b) The torque required to prevent the sprinkler from
Reconsider Prob. 6–66. The maximum efficiency of the turbine occurs when β = 180°, but this is not practical. Investigate the effect of β on the power generation by allowing it to vary from 0° to 180°. Do you think we are wasting a large fraction of power by using buckets with a β of
Repeat Prob. 6–71 for the case of unequal arms—the left one being 60 cm and the right one 20 cm from the axis of rotation.Data from Exercises 71.Water enters vertically and steadily at a rate of 10 L/s into the sprinkler shown in Fig. P6–71. Both water jets have a diameter of 1.2 cm.
A walnut with a mass of 50 g requires a force of 200 N applied continuously for 0.002 s to be cracked. If walnuts are to be cracked by dropping them from a high place onto a hard surface, determine the minimum height required. Disregard air friction.
Show that the force exerted by a liquid jet on a stationary nozzle as it leaves with a velocity V is proportional to V2 or, alternatively, to ṁ2. Assume the jet stream is perpenticular to the incoming liquid flow line.
A horizontal water jet with a flow rate of V̇ and cross-sectional area of A drives a covered cart of mass mc along a level and nearly frictionless path. The jet enters a hole at the rear of the cart and all water that enters the cart is retained, increasing the system mass. The relative velocity
Water accelerated by a nozzle enters the impeller of a turbine through its outer edge of diameter D with a velocity of V making an angle a with the radial direction at a mass flow rate of ṁ. Water leaves the impeller in the radial direction. If the angular speed of the turbine shaft is ṅ, show
Water enters a two-armed lawn sprinkler along the vertical axis at a rate of 75 L/s, and leaves the sprinkler nozzles as 2-cm diameter jets at an angle of θ from the tangential direction, as shown in Fig. P6–92. The length of each sprinkler arm is 0.52 m. Disregarding any frictional effects,
Reconsider Prob. 6–92. For the specified flow rate, investigate the effect of discharge angle θ on the rate of rotation ṅ by varying u from 0° to 90° in increments of 10°. Plot the rate of rotation versus θ, and discuss your results.Data from Problem 92Water enters a two-armed lawn
A stationary water tank of diameter D is mounted on wheels and is placed on a nearly frictionless level surface. A smooth hole of diameter Do near the bottom of the tank allows water to jet horizontally and rearward and the water jet force propels the system forward. The water in the tank is much
An orbiting satellite has a mass of 3400 kg and is traveling at a constant velocity of V0. To alter its orbit, an attached rocket discharges 100 kg of gases from the reaction of solid fuel at a speed of 3000 m/s relative to the satellite in a direction opposite V0. The fuel discharge rate is
Water enters a mixed flow pump axially at a rate of 0.3 m3/s and at a velocity of 7 m/s, and is discharged to the atmosphere at an angle of 75° from the horizontal, as shown in Fig. P6–96. If the discharge flow area is half the inlet area, determine the force acting on the shaft in the axial
Water flows steadily through a splitter as shown in Fig. P6–97 with D1 = D2 = 12 cm, D3 = 10 cm. If the pressure readings at the inlet and outlets of the splitter are P1 = 100 kPa, P2 = 90 kPa and P3 = 80 kPa, determine external force needed to hold the device fixed. Disregard the weight
Water is discharged from a pipe through a 1.2-m long 5-mm wide rectangular slit underneath of the pipe. Water discharge velocity profile is parabolic, varying from 3 m/s on one end of the slit to 7 m/s on the other, as shown in Fig. P6–98. Determine (a) The rate of discharge through the slit(b)
When determining the thrust developed by a jet engine, a wise choice of control volume is(a) Fixed control volume (b) Moving control volume(c) Deforming control volume (d) Moving or deforming control volume (e) None of these
Consider an airplane cruising at 850 km/h to the right. If the velocity of exhaust gases is 700 km/h to the left relative to the ground, the velocity of the exhaust gases relative to the nozzle exit is(a) 1550 km/h (b) 850 km/h (c) 700 km/h(d) 350 km/h (e) 150 km/h
Consider water flow through a horizontal, short garden hose at a rate of 30 kg/min. The velocity at the inlet is 1.5 m/s and that at the outlet is 14.5 m/s. Disregard the weight of the hose and water. Taking the momentum-flux correction factor to be 1.04 at both the inlet and the outlet, the
Consider water flow through a horizontal, short garden hose at a rate of 30 kg/min. The velocity at the inlet is 1.5 m/s and that at the outlet is 11.5 m/s. The hose makes a 180° turn before the water is discharged. Disregard the weight of the hose and water. Taking the momentum-flux correction
A water jet strikes a stationary vertical plate horizontally at a rate of 5 kg/s with a velocity of 35 km/h. Assume the water stream moves in the vertical direction after the strike. The force needed to prevent the plate from moving horizontally is(a) 15.5 N (b) 26.3 N (c) 19.7 N (d) 34.2 N (e)
Consider water flow through a horizontal, short garden hose at a rate of 40 kg/min. The velocity at the inlet is 1.5 m/s and that at the outlet is 16 m/s. The hose makes a 90° turn to a vertical direction before the water is discharged. Disregard the weight of the hose and water. Taking the
Consider water flow through a horizontal, short pipe at a rate of 80 kg/min. The velocity at the inlet is 1.5 m/s and that at the outlet is 16.5 m/s. The pipe makes a 90° turn to a vertical direction before the water is discharged. Disregard the weight of the pipe and water. Taking the
A water jet strikes a stationary horizontal plate vertically at a rate of 18 kg/s with a velocity of 24 m/s. The mass of the plate is 10 kg. Assume the water stream moves in the horizontal direction after the strike. The force needed to prevent the plate from moving vertically is(a) 192 N (b) 240
The velocity of wind at a wind turbine is measured to be 6 m/s. The blade span diameter is 24 m and the efficiency of the wind turbine is 29 percent. The density of air is 1.22 kg/m3. The horizontal force exerted by the wind on the supporting mast of the wind turbine is(a) 2524 N (b) 3127 N (c)
The velocity of wind at a wind turbine is measured to be 8 m/s. The blade span diameter is 12 m. The density of air is 1.2 kg/m3. If the horizontal force exerted by the wind on the supporting mast of the wind turbine is 1620 N, the efficiency of the wind turbine is(a) 27.5% (b) 31.7% (c)
The shaft of a turbine rotates at a speed of 800 rpm. If the torque of the shaft is 350 N·m, the shaft power is(a) 112 kW (b) 176 kW (c) 293 kW (d) 350 kW(e) 405 kW
A 3-cm-diameter horizontal pipe attached to a surface makes a 90° turn to a vertical upward direction before the water is discharged at a velocity of 9 m/s. The horizontal section is 5 m long and the vertical section is 4 m long. Neglecting the mass of the water contained in the pipe, the bending
A 3-cm-diameter horizontal pipe attached to a surface makes a 90° turn to a vertical upward direction before the water is discharged at a velocity of 6 m/s. The horizontal section is 5 m long and the vertical section is 4 m long. Neglecting the mass of the pipe and considering the weight of the
A large lawn sprinkler with four identical arms is to be converted into a turbine to generate electric power by attaching a generator to its rotating head. Water enters the sprinkler from the base along the axis of rotation at a rate of 15 kg/s and leaves the nozzles in the tangential direction at
Consider the impeller of a centrifugal pump with a rotational speed of 900 rpm and a flow rate of 95 kg/min. The impeller radii at the inlet and outlet are 7 cm and 16 cm, respectively. Assuming that the tangential fluid velocity is equal to the blade angular velocity both at the inlet and the
Water enters the impeller of a centrifugal pump radially at a rate of 450 L/min when the shaft is rotating at 400 rpm. The tangential component of absolute velocity of water at the exit of the 70-cm outer diameter impeller is 55 m/s. The torque applied to the impeller is(a) 144 N·m (b) 93.6
List the seven primary dimensions. What is significant about these seven?
What is the difference between a dimension and a unit? Give three examples of each.
Write the primary dimensions of the universal ideal gas constant Ru. (Use the ideal gas law, PV = nRuT where P is pressure, V is volume, T is absolute temperature, and n is the number of moles of the gas.)
When performing a dimensional analysis, one of the first steps is to list the primary dimensions of each relevant parameter. It is handy to have a table of parameters and their primary dimensions. We have started such a table for you (Table P7–5), in which we have included some of the basic
Write the primary dimensions of each of the following variables from the field of thermodynamics, showing all your work: (a) Energy E; (b) Specific energy e = E/m; (c) Power Ẇ.
Consider the table of Prob. 7–5 where the primary dimensions of several variables are listed in the mass– length–time system. Some engineers prefer the force–length–time system (force replaces mass as one of the primary dimensions). Write the primary dimensions of three of these (density,
On a periodic chart of the elements, molar mass (M), also called atomic weight, is often listed as though it were a dimensionless quantity (Fig. P7–7). In reality, atomic weight is the mass of 1 mol of the element. For example, the atomic weight of nitrogen Mnitrogen = 14.0067. We interpret this
We define the specific ideal gas constant Rgas for a particular gas as the ratio of the universal gas constant and the molar mass (also called molecular weight) of the gas, Rgas = Ru/M. For a particular gas, then, the ideal gas law is written as follows:where P is pressure, V is volume, m is mass,
Some authors prefer to use force as a primary dimension in place of mass. In a typical fluid mechanics problem, then, the four represented primary dimensions m, L, t, and T are replaced by F, L, t, and T. The primary dimension of force in this system is {force} = {F}. Using the results of Prob.
The moment of force (M(vector)) is formed by the cross product of a moment arm (r(vector)) and an applied force (F(vector)), as sketched in Fig. P7–10. What are the primary dimensions of moment of force? List its units in primary SI units and in primary English units.Figure 7-10 M=rX F Point O F
What are the primary dimensions of electric voltage (E)?
You are probably familiar with Ohm’s law for electric circuits (Fig. P7–12), where ΔE is the voltage difference or potential across the resistor, I is the electric current passing through the resistor, and R is the electrical resistance. What are the primary dimensions of electrical
Write the primary dimensions of each of the following variables, showing all your work: (a) Acceleration a;(b) Angular velocity ω; (c) Angular acceleration α.
Angular momentum, also called moment of momentum (H(vector)), is formed by the cross product of a moment arm (r(vector)) and the linear momentum (mV(vector)) of a fluid particle, as sketched in Fig. P7–14. What are the primary dimensions of angular momentum? List the units of angular momentum in
Thermal conductivity k is a measure of the ability of a material to conduct heat (Fig. P7–16). For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed aswhere Q̇ conduction is the rate of heat transfer and A is
Write the primary dimensions of each of the following variables, showing all your work: (a) Specific heat at constant pressure cp; (b) Specific weight ρg; (c) Specific enthalpy h.
Write the primary dimensions of each of the following variables from the study of convection heat transfer (Fig. P7–17), showing all your work: (a) Heat generation rate ġ;(b) Heat flux q̇.(c) Heat transfer coefficient hFIGURE P7–17 Too Ts ġ h = T₁ - Too ·00
Thumb through the appendices of this book and/or your thermodynamics book, and find three properties or constants not mentioned in Probs. 7–1 to 7–17. List the name of each property or constant and its English units. Then write out the primary dimensions of each property or constant.Data from
Explain the law of dimensional homogeneity in simple terms.
In Chap. 4, we defined the material acceleration, which is the acceleration following a fluid particle,(a) What are the primary dimensions of the gradient operator ∇(vector) ?(b) Verify that each additive term in the equation has the same dimensions. a(x, y, z, 1) = = av at + (V.)
Newton’s second law is the foundation for the differential equation of conservation of linear momentum (to be discussed in Chap. 9). In terms of the material acceleration following a fluid particle (Fig. P7–21), we write Newton’s second law as follows:Or, dividing both sides by the mass m of
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