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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Liquid flows with a free surface around a bend. The liquid is inviscid and incompressible, and the flow is steady and irrotational. The velocity varies with the radius across the flow as V = 1/r m/s,
A two-dimensional flow field is defined by u = x2 – y2 and v = –2xy. Is the flow rotational or irrotational?
The velocity components for a two-dimensional flow arewhere C is a constant. Is the flow irrotational? Cx Cy (y + x) v = (x² + y)
The u and v velocity components of a flow field are given by u = –ωy and v = ωx. Determine the vorticity and the rate of rotation of flow field.
The vector V = 10xi – 10yj represents a two-dimensional velocity field. Is the flow irrotational?
Consider a spherical fluid particle in an inviscid fluid (no shear stresses). If pressure and gravitational forces are the only forces acting on the particle, can they cause the particle to rotate?
What is meant by rotation of a fluid particle? Use a sketch to explain.
You need to measure air flow velocity. You order a commercially available Pitot-static tube, and the accompanying instructions state that the airflow velocity is given by where hv is the
A Pitot-static tube is used to measure the airspeed of an airplane. The Pitot tube is connected to a pressure-sensing device calibrated to indicate the correct airspeed when the temperature is 17°C
A rugged instrument used frequently for monitoring gas velocity in smokestacks consists of two open tubes oriented to the flow direction as shown and connected to a manometer. The pressure
Water in a flume is shown for two conditions. If the depth d is the same for each case, will gage A read greater or less than gage B? Explain. d A Pressure gage (a) V = 3 m/s d Pressure gage B (b)
This navy surveillance sphere is being tested for the pressure field that will be induced in front of it as a function of velocity. Velocimeters in the test basin show that when VA = 14 m/s, the
A device used to measure the velocity of fluid in a pipe consists of a cylinder, with a diameter much smaller than the pipe diameter, mounted in the pipe with pressure taps at the forward stagnation
The “spherical” Pitot probe shown is used to measure the flow velocity in hot water (ρ = 965 kg/m3). Pressure taps are located at the forward stagnation point and at 90° from the forward
The flow-metering device shown consists of a stagnation probe at station 2 and a static pressure tap at station 1. The velocity at station 2 is 1.5 times that at station 1. Air with a density of 1.2
A Pitot-static tube is used to measure the gas velocity in a duct. A pressure transducer connected to the Pitot tube registers a pressure difference of 3.0 psi. The density of the gas in the duct is
A Pitot-static tube used to measure air velocity is connected to a pressure gage. If the air temperature is 200°F at standard atmospheric pressure, and if the gage reads a differential pressure of
A Pitot-static tube used to measure air velocity is connected to a pressure gage. If the air temperature is 10°C at standard atmospheric pressure at sea level, and if the gage reads a differential
A Pitot-static tube is used to measure the velocity at the center of a 12 in. pipe. If kerosene at 68°F is flowing and the deflection on a mercury-kerosene manometer connected to the Pitot tube is
Two Pitot-static tubes are shown. The one on the top is used to measure the velocity of air, and it is connected to an air-water manometer as shown. The one on the bottom is used to measure the
To measure air velocity in a food-drying plant (T = 160°F, p = 14 psia), an air-water manometer is connected to a Pitot-static tube. When the manometer deflects 4 in., what is the velocity?
A glass tube is inserted into a flowing stream of water with one opening directed upstream and the other end vertical. If the water velocity, VA is 6.6 m/s, how high will the water rise, h? h Water V
A Pitot tube is placed in an open channel as shown. What is the velocity VA (m/s) when height h is 15 cm?
A Pitot-static tube is mounted on an airplane to measure airspeed. At an altitude of 10,000 ft , where the temperature is 23°F and the pressure is 9 psia, a pressure difference corresponding to 8
A stagnation tube placed in a river (select all that apply)a. Can be used to determine air pressureb. Can be used to determine water velocityc. Measures kinetic pressure + static pressure
Kerosene at 20°C flows through a contraction section as shown. A pressure gage connected between the upstream pipe and throat section shows a pressure difference of 25 kPa. The gasoline velocity in
Water flows through a vertical contraction (venturi) section. Piezometers are attached to the upstream pipe and minimum area section as shown. The mean velocity in the pipe is V = 5 ft /s. The
The tank shown is used to pressurize a water-fertilizer solution for delivery from a sprayer. The tank is pressurized at p = 15 kPa gage. Height h is 0.8 m. What is the velocity (m/s) of the
An engineer is designing a fountain, as shown, and will install a nozzle that can produce a vertical jet. How high (h) will the water in the fountain rise if Vn = 26 m/s at h = 0? V.
Describe in your own words how an aspirator works.
The closed tank shown, which is full of liquid, is accelerated downward at 23 g and to the right at 1g. Here L = 2.5 m, H = 3 m, and the liquid has a specific gravity of 1.3. Determine pC – pA and
The closed tank shown, which is full of liquid, is accelerated downward at 1.5g and to the right at 0.9g. Here L = 3 ft , H = 4 ft , and the specific gravity of the liquid is 1.2. Determine pC – pA
If the velocity varies linearly with distance through this water nozzle, what is the pressure gradient, dp/dx, halfway through the nozzle? Assume ρ = 62.4 lbm/ft 3. 30 ft/s 80 ft/s 1 ft-
A liquid with a specific weight of 100 lbf/ft3 is in the conduit. This is a special kind of liquid that has zero viscosity. The pressures at points A and B are 170 psf and 100 psf, respectively.
Water (ρ = 1000 kg/m3) is accelerated from rest in a horizontal pipe that is 80 m long and 30 cm in diameter. If the acceleration rate (toward the downstream end) is 5 m/s2, what is the pressure at
What pressure gradient is required to accelerate water (ρ = 1000 kg/m3) in a horizontal pipe at a rate of 7.7 m/s2?
Water (ρ = 62.4 lbm/ft3) stands at a depth of 6 ft in a vertical pipe that is open at the top and closed at the bottom by a piston. What upward acceleration of the piston is necessary to create a
The hypothetical liquid in the tube shown in the figure has zero viscosity and a specific weight of 10 kN/m3. If pB – pA is equal to 8 kPa, one can conclude that the liquid in the tube is
What pressure gradient is required to accelerate kerosene (SG = 0.81) vertically upward in a vertical pipe at a rate of 0.4 g?
What are the differences between a force due to weight and a force due to pressure? Explain.
State Newton’s second law of motion. What are the limitations on the use of Newton’s second law? Explain.
The velocity of water flow in the nozzle shown is given by the following expression:V = 2t/(1 − 0.5x/L)2, where V = velocity in feet per second, t = time in seconds, x = distance along the nozzle,
In Prob. 4.26 the velocity varies linearly with time throughout the nozzle. The velocity at the base is 1t (ft /s) and at the tip is 4t (ft /s). What is the local acceleration midway along the nozzle
The nozzle in the figure is shaped such that the velocity of the fluid varies linearly from the base of the nozzle to its tip. Assuming quasi-one-dimensional flow, what is the convective acceleration
In this fl ow passage, the velocity is varying with time. The velocity varies with time at section A-A asAt time t = 0.50 s, it is known that at section A-A the velocity gradient in the s direction
Part 1. Consider the equation for the distance between the CP and the centroid of a submerged panel (Eq. (3.33)). In that equation, ycp isa. The vertical distance from the water surface to the CP.b.
Using §3.2 and other resources, answer the following questions. Strive for depth, clarity, and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of
The local atmospheric pressure is 91 kPa. A gage on an oxygen tank reads a pressure of 250 kPa gage. What is the pressure in the tank in kPa abs?
The surface tension of a liquid is being measured with a ring as shown. The ring has an outside diameter of 10 cm and an inside diameter of 9.5 cm. The mass of the ring is 10 g. The force required to
A drop of water at 20°C is forming under a solid surface. The configuration just before separating and falling as a drop is shown in the figure. Assume the forming drop has the volume of a
Consider a soap bubble 2 mm in diameter and a droplet of water, also 2 mm in diameter. If the value of the surface tension for the film of the soap bubble is assumed to be the same as that for water,
Capillary rise can be used to describe how far water will rise above a water table because the interconnected pores in the soil act like capillary tubes. This means that deep-rooted plants in the
By measuring the capillary rise in a tube, one can calculate the surface tension. The surface tension of water varies linearly with temperature from 0.0756 N/m at 0°C to 0.0589 N/m at 100°C. Size a
What is the pressure within a d = 0.75 mm spherical droplet of water, relative to the atmospheric pressure outside the droplet?
Calculate the maximum capillary rise of water between two vertical glass plates spaced 1 mm apart.
A water column in a glass tube is used to measure the pressure in a pipe. The tube is 1/2 in. in diameter. How much of the water column is due to surface-tension effects? What would be the
A water bug is suspended on the surface of a pond by surface tension (water does not wet the legs). Th e bug has six legs, and each leg is in contact with the water over a length of 3 mm. What is the
This problem involves a cylinder falling inside a pipe that is filled with oil, as depicted in the figure. The small space between the cylinder and the pipe is lubricated with an oil film that has
Determine the forces in the x- and y-directions needed to hold this fixed vane, which turns the oil jet (SG = 0.9) in a horizontal plane. Here V1 = 29 m/s, V2 = 33 m/s, and Q = 0.9 m3/s. y Oil (SG =
Solve Prob. 6.23 for V1 = 70 ft /s, V2 = 65 ft /s, and Q = 1.5 cfs.Data from Prob. 6.23Determine the forces in the x- and y-directions needed to hold this fixed vane, which turns the oil jet (SG =
This planar water jet (60°F) is deflected by a fixed vane. What are the x- and y-components of force per unit width needed to hold the vane stationary? Neglect gravity. 0.2 ft 60° 40 ft/s 30° 0.1
A water jet with a speed of 60 ft/s and a mass flow rate of 40 lbm/s is turned 30° by a fixed vane. Find the force of the water jet on the vane. Neglect gravity. 30°
Water (ρ = 1000 kg/m3) strikes a block as shown and is deflected 30°. The flow rate of the water is 15.1 kg/s, and the inlet velocity is V = 16 m/s. The mass of the block is 1 kg. The coefficient
For the situation described in Prob. 6.27, find the maximum inlet velocity (V) such that the block will not slip.Data from Prob. 6.27,Water (ρ = 1000 kg/m3) strikes a block as shown and is deflected
Plate A is 50 cm in diameter and has a sharp-edged orifice at its center. A water jet (at 10°C) strikes the plate concentrically with a speed of 60 m/s. What external force is needed to hold the
A cone that is held stable by a wire is free to move in the vertical direction and has a jet of water (at 10°C) striking it from below. The cone weighs 30 N. The initial speed of the jet as it comes
A vane on this moving cart deflects a 15-cm-diameter water (ρ = 1000 kg/m3) jet as shown. The initial speed of the water in the jet is 50 m/s, and the cart moves at a speed of 3 m/s. If the vane
Refer to the cart of Prob. 6.32. If the cart speed is constant at 5 ft/s, and if the initial jet speed is 60 ft /s, and jet diameter = 0.15 ft, what is the rolling resistance of the cart? (ρ = 62.4
The water (ρ = 1000 kg/m3) in this jet has a speed of 60 m/s to the right and is deflected by a cone that is moving to the left with a speed of 5 m/s. Th e diameter of the jet is 10 cm. Determine
This two-dimensional water (at 50°F) jet is deflected by the two-dimensional vane, which is moving to the right with a speed of 60 ft /s. The initial jet is 0.30 ft thick (vertical dimension), and
Assume that the scoop shown, which is 20 cm wide, is used as a braking device for studying deceleration effects, such as those on space vehicles. If the scoop is attached to a 1000 kg sled that is
This snowplow clears a swath of snow (SG = 0.20) that is 4 in. deep (d = 4 in.) and 2 ft wide (B = 2 ft). The snow leaves the blade in the direction indicated in the sketches. Neglecting friction
High-speed water jets are used for specialty cutting applications. The pressure in the chamber is approximately 60,000 psig. Using the Bernoulli equation, estimate the water speed exiting the nozzle
Water at 60°F flows through a nozzle that contracts from a diameter of 12 in. to 1 in. The pressure at section 1 is 2500 psfg, and atmospheric pressure prevails at the exit of the jet. Calculate the
Water at 15°C flows through a nozzle that contracts from a diameter of 15 cm to 2 cm. Th e exit speed is v2 = 10 m/s, and atmospheric pressure prevails at the exit of the jet. Calculate the pressure
Water (at 50°F) flows through this nozzle at a rate of 25 cfs and discharges into the atmosphere. D1 = 20 in., and D2 = 9 in. Determine the force required at the flange to hold the nozzle in place.
Solve Prob. 6.42 using the following values: Q = 0.30 m3/s, D1 = 30 cm, and D2 = 10 cm. (ρ = 1000 kg/m3.)Data from Prob. 6.42 Water (at 50°F) flows through this nozzle at a rate of 25 cfs and
This “double” nozzle discharges water (ρ = 62.4 lbm/ft3) into the atmosphere at a rate of 16 cfs. If the nozzle is lying in a horizontal plane, what x-component of force acting through the
This “double” nozzle discharges water (at 10°C) into the atmosphere at a rate of 0.65 m3/s. If the nozzle is lying in a horizontal plane, what x-component of force acting through the flange
A rocket-nozzle designer is concerned about the force required to hold the nozzle section on the body of a rocket. The nozzle section is shaped as shown in the figure. The pressure and velocity at
Water (ρ = 62.4 lbm/ft 3) is discharged from the two-dimensional slot shown at the rate of 8 cfs per foot of slot. Determine the pressure p at the gage and the water force per foot on the vertical
Water (at 10°C) is discharged from the two-dimensional slot shown at the rate of 0.40 m3/s per meter of slot. Determine the pressure p at the gage and the water force per meter on the vertical end
This spray head discharges water (ρ = 62.4 lbm/ft3) at a rate of 4 ft3/s. Assuming irrotational flow and an efflux speed of 58 ft/s in the free jet, determine what force acting through the bolts of
Two circular water (ρ = 62.4 lbm/ft3) jets (d = 0.5 in.) issue from this unusual nozzle. If Vj = 80.2 ft/s, what force is required at the flange to hold the nozzle in place? The pressure in the 4
Liquid (SG = 1.2) enters the “black sphere” through a 2 in. pipe with velocity of 50 ft/s and a pressure of 60 psig. It leaves the sphere through two jets as shown. The velocity in the vertical
Liquid (SG = 1.5) enters the “black sphere” through a 5 cm pipe with a velocity of 10 m/s and a pressure of 400 kPa. It leaves the sphere through two jets as shown. The velocity in the vertical
A hot gas stream enters a uniform-diameter return bend as shown. The entrance velocity is 100 ft /s, the gas density is 0.02 lbm/ft3, and the mass flow rate is 2 lbm/s. Water is sprayed into the duct
Assume that the gage pressure p is the same at sections 1 and 2 in the horizontal bend shown in the figure. The fluid flowing in the bend has density ρ, discharge Q, and velocity V. The
The pipe shown has a 180° vertical bend in it. The diameter D is 1.25 ft , and the pressure at the center of the upper pipe is 15 psig. If the flow in the bend is 40 cfs, what external force will be
The pipe shown has a 180° horizontal bend in it as shown, and D is 20 cm. The discharge of water (ρ = 1000 kg/m3) in the pipe and bend is 0.35 m3/s, and the pressure in the pipe and bend is 100 kPa
Water (at 50°F) flows in the 90° horizontal bend at a rate of 12 cfs and discharges into the atmosphere past the downstream flange. The pipe diameter is 1 ft . What force must be applied at the
The gage pressure throughout the horizontal 90° pipe bend is 300 kPa. If the pipe diameter is 1.5 m and the water (at 10°C) flow rate is 10 m3/s, what x-component of force must be applied to the
This 30° vertical bend in a pipe with a 1.5 ft diameter carries water (ρ = 62.4 lbm/ft 3) at a rate of 31.4 cfs. If the pressure p1 is 10 psi at the lower end of the bend, where the elevation is
This bend discharges water (ρ = 1000 kg/m3) into the atmosphere. Determine the force components at the flange required to hold the bend in place. The bend lies in a horizontal plane. Assume viscous
This nozzle bends the flow from vertically upward to 30° with the horizontal and discharges water (γ = 62.4 lbf/ft 3) at a speed of V = 130 ft/s. The volume within the nozzle itself is 1.8 ft3, and
A pipe 1 ft in diameter bends through an angle of 135°. The velocity of flow of gasoline (SG = 0.8) is 15 ft/s, and the pressure is 10 psig in the bend. What external force is required to hold the
A 4-in. horizontal pipe has a 180° bend in it. If the rate of flow of water (60°F) in the bend is 8 cfs and the pressure therein is 20 psig, what external force in the original direction of flow is
A pipe 15 cm in diameter bends through 135°. The velocity of flow of gasoline (SG = 0.8) is 8 m/s, and the pressure is 100 kPa gage throughout the bend. Neglecting gravitational force, determine the
A horizontal reducing bend turns the flow of water (ρ = 1000 kg/m3) through 60°. The inlet area is 0.001 m2, and the outlet area is 0.0001 m2. The water from the outlet discharges into the
Water (at 10°C) flows in a duct as shown. The inlet water velocity is V1 = 25 m/s. The cross-sectional area of the duct is 0.1 m2. Water is injected normal to the duct wall at the rate of 500 kg/s

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