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engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

The annular venturi meter is useful for metering flows in pipe systems for which upstream calming distances are limited. The annular venturi meter consists of a cylindrical section mounted inside a
The flow pattern through the pipe contraction is as shown, and the Q of water is 60 cfs. For d = 2 ft and D = 6 ft , what is the pressure at point B if the pressure at point C is 3200 psf? C E d 20°
Water is flowing from Location 1 to 2 in this pipe expansion. D1 and V1 are known at the inlet. D2 and p2 are known at the outlet. What equation(s) do you need to solve for the inlet pressure p1?
Air is flowing from a ventilation duct (cross section 1) as shown, and is expanding to be released into a room at cross section 2. The area at cross section 2, A2, is three times A1. Assume that the
Gas is flowing from Location 1 to 2 in the pipe expansion shown. The inlet density, diameter and velocity are ρ1, D1, and V1 respectively. If D2 is 2D1 and V2 is half of V1, what is the magnitude of
A cylindrical-port rocket motor has a grain design consisting of a cylindrical shape as shown. The curved internal surface and both ends burn. The solid propellant surface regresses uniformly at 1
An end-burning rocket motor has a chamber diameter of 10 cm and a nozzle exit diameter of 8 cm. The density of the solid propellant is 1770 kg/m3, and the propellant surface regresses at the rate of
To prepare for problems 5.79 and 5.80 use the Internet or other resources and define the following terms in the context of rocket propulsion: (a) Solid fuel, (b) Grain,(c) Surface
A spherical tank with a radius (R) of 0.5 m is half filled with water. A port at the bottom of the tank is opened to drain the tank. Th e hole diameter is 1 cm, and the velocity of the water draining
Water is draining from a pressurized tank as shown in the figure. The exit velocity is given bywhere p is the pressure in the tank, ρ is the water density, and h is the elevation of the water
How long will it take the water surface in the tank shown to drop from h = 3 m to h = 50 cm? 60 cm diameter h 3 cm diameter V= V2gh
In the flow through an orifice shown in the diagram, theflow goes through a minimum area downstream of the orifice. This is called the “vena contracta.” The ratio of the flow area atthe vena
The globe valve shown in the figure is a very common device to control flow rate. The flow comes through the pipe at the left and then passes through a minimum area formed by the disc and valve seat.
A pipe with a series of holes as shown in the figure is used in many engineering systems to distribute gas into a system. The volume flow rate through each hole depends on the pressure difference
Oxygen and methane are mixed at 204 kPa absolute pressure and 100°C. The velocity of the gases into the mixer is 8 m/s. The density of the gas leaving the mixer is 2.2 kg/m3. Determine the exit
Assuming that complete mixing occurs between the two inflows before the mixture discharges from the pipe at C, find the mass rate of flow, the velocity, and the specific gravity of the mixture in the
An open tank has a constant inflow of 20 ft3/s. A 1.0-ft-diameter drain provides a variable outflow velocity Vout equal to √(2gh) ft/s. What is the equilibrium height heq of the liquid in the tank?
A stationary nozzle discharges water against a plate moving toward the nozzle at half the jet velocity. When the discharge from the nozzle is 5 cfs, at what rate will the plate deflect water?
A lake with no outlet is fed by a river with a constant flow of 1800 ft 3/s. Water evaporates from the surface at a constant rate of 12 ft3/s per square mile surface area. Th e area varies with depth
Given: Flow velocities as shown in the figure and water surface elevation (as shown) at t = 0 s. At the end of 22 s, will the water surface in the tank be rising or falling, and at what speed? 2 ft
Is the tank in the figure filling or emptying? At what rate is the water level rising or falling in the tank? 6 ft diameter 3 in. diameter 4 in. diameter V= 4 ft/s Water V= 10 ft/s 6 in, diameter V =
Two pipes, A and B, are connected to an open water tank. The water is entering the bottom of the tank from pipe A at 10 cfm. The water level in the tank is rising at 1.0 in./min, and the surface area
For a steady flow of gas in the conduit shown, what is the mean velocity at section 2? 1.1 m diameter 56 cm diameter - Ip, = 1.8 kg/m Tp, = 2.0 kg/m V = 16 m/s
What is the velocity of the flow of water in leg B of the tee shown in the figure? A B 4 m diameter V=? V= 6 m/s 2 m diameter - 4 m/s
Water flows in a 12 in. pipe that is connected in series with a 4 in. pipe. If the rate of flow is 927 gpm (gallons per minute), what is the mean velocity in each pipe?
A 30 cm pipe divides into a 20 cm branch and a 8 cm branch. If the total discharge is 0.45 m3/s and if the same mean velocity occurs in each branch, what is the discharge in each branch?
A rectangular air duct 21 cm by 50 cm carries a flow of 1.2 m3/s. Determine the velocity in the duct. If the duct tapers to 9 cm by 39 cm, what is the velocity in the latter section? Assume constant
This circular tank of water is being filled from a pipe as shown. The velocity of flow of water from the pipe is 10 ft /s. What will be the rate of rise of the water surface in the tank? Diameter = 1
A mechanical pump is used to pressurize a bicycle tire. The in flow to the pump is 0.4 cfm. The density of the air entering the pump is 0.075 lbm/ft3. The inflated volume of a bicycle tire is 0.050
A tank has a hole in the bottom with a cross-sectional area of 0.0025 m2 and an inlet line on the side with a cross-sectional area of 0.0025 m2, as shown. The cross-sectional area of the tank is 0.1
All the conditions of Prob. 5.52 are the same except that h = 1 cm and the discharge is given as Q = Q0(t/t0), where Q0 = 0.1 m3/s and t0 = 1 s. For the additional conditions, what will be the
Air discharges downward in the pipe and then outward between the parallel disks. Assuming negligible density change in the air, derive a formula for the acceleration of air at point A, which is a
In a food-drying facility, a constant-diameter heated pipe is used to raise the temperature of air. At the pipe entrance, the velocity is 12 m/s, the pressure is 100 kPa absolute, and the temperature
During the production of biodiesel, glycerin is a waste product and is collected by gravity separation because its SG (1.26) is much higher than that of biodiesel. Glycerin is withdrawn from the
Two streams discharge into a pipe as shown. The flows are incompressible. The volume flow rate of stream A into the pipe is given by QA = 0.01t m3/s and that of stream B by QB = 0.006 t2 m3/s, where
Both pistons are moving to the left , but piston A has a speed twice as great as that of piston B. Is the water level in the tank (a) Rising, (b) Not moving up or down, or(c) Falling?
Two pipes are connected together in series. The diameter of one pipe is three (3) times the diameter of the second pipe. With liquid flowing in the pipes, the velocity in the large pipe is 4 m/s.
Air is pumped into one end of a tube at a certain mass flow rate. Is it necessary that the same mass flow rate of air comes out the other end of the tube? Explain.
Water flows through a full pipe. Is it possible for the volume flow rate into the pipe to be different than the flow rate out of the pipe? Explain.
Consider the simplified form of the continuity equation, Eq. 5.29. An engineer is using this equation to find the discharge QC of a creek at the confluence with a large river because she has
The law of conservation of mass for a closed system requires that the mass of the system isa. Constantb. Zero
For cases a and b shown in the figure, respond to the following questions and statements concerning the application of the Reynolds transport theorem to the continuity equation.a. What is the value
The piston in the cylinder is moving up. Assume that the control volume is the volume inside the cylinder above the piston (the control volume changes in size as the piston moves). A gaseous mixture
Gas flows into and out of the chamber as shown. For the conditions shown, which of the following statement(s) are true of the application of the control volume equation to the continuity principle?a.
What is the purpose of the Reynolds transport theorem?
What is a control surface and a control volume? Can mass pass through a control surface?
What type of property do you get when you divide an extensive property by another extensive property—extensive or intensive?
State whether each of the following quantities is extensive or intensive:a. Massb. Volumec. Densityd. Energye. Specific energy
What is the difference between an intensive and extensive property? Give an example of each.
Read §4.2 and §5.2 and use the Internet to find answers to the following questions:a. What does the Lagrangian approach mean? What are three real-world examples that illustrate the Lagrangian
The mean velocity of water in a 5-in. pipe is 9 ft /s. Determine the flow rate in slugs per second, gallons per minute, and cubic feet per second if T = 60°F.
The cross section of a heat exchanger consists of three circular pipes inside a larger pipe. The internal diameter of the three smaller pipes is DS = 1.5 cm, and their pipe wall thicknesses are each
A shell and tube heat exchanger consists of a one pipe inside another pipe as shown. The liquid flows in opposite directions in each pipe. If the speed and discharge of the liquid is the same in each
Water from a pipeline is diverted into a weigh tank for 15 min. The increased weight in the tank is 4765 lbf. What is the average flow rate in gallons per minute and in cubic feet per second? Assume
Water flows through a 17 cm pipeline at 1022 kg/min. Calculate the mean velocity in meters per second if T = 20°C.
Water flows through a 4.0 in. diameter pipeline at 75 lbm/min. Calculate the mean velocity. Assume T = 60°F.
The velocity of flow in a circular pipe varies according to the equation V/Vc = (1 – r2/r2 0)n, where Vc is the centerline velocity, r0 is the pipe radius, and r is the radial distance from the
The hypothetical water velocity in a V-shaped channel (see the accompanying figure) varies linearly with depth from zero at the bottom to maximum at the water surface. Determine the discharge if the
An empirical equation for the velocity distribution in a horizontal, rectangular, open channel is given by u = umax (y/d)n, where u is the velocity at a distance y meters above the floor of the
Water enters the lock of a ship canal through 180 ports, each port having a 2 ft by 2 ft cross section. The lock is 900 ft long and 105 ft wide. The lock is designed so that the water surface in it
If the velocity in the channel of Problem 5.18 is given as u = 8[exp(y) – 1] m/s and the channel width is 2 m, what is the discharge in the channel and what is the mean velocity?Data from Problem
The rectangular channel shown is 1.2 m wide. What is the discharge in the channel? Vertical depth = 1m 1/3 u = y"3 m/s Water 30°
The velocity at section A-A is 15 ft /s, and the vertical depth y at the same section is 3 ft . If the width of the channel is 40 ft , what is the discharge in cubic feet per second? A A 30°
Air enters this square duct at section 1 with the velocity distribution as shown. Note that the velocity varies in the y direction only (for a given value of y, the velocity is the same for all
In Problem 5.14, if Vmax = 8 m/s, Vmin = 6 m/s, and D = 2 m, what is the discharge in cubic meters per second and the mean velocity?Data from Problem 5.14,Water flows in a pipe that has a 4 ft
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity distribution: The velocity is maximum at the centerline and decreases linearly with r to a minimum at the pipe
Water flows in a two-dimensional channel of width W and depth D as shown in the diagram. The hypothetical velocity profile for the water is where Vs is the velocity at the water surface midway
The hypothetical velocity distribution in a circular duct is where r is the radial location in the duct, R is the duct radius, and V0 is the velocity on the axis. Find the ratio of the mean
A heating and air-conditioning engineer is designing a system to move 1000 m3 of air per hour at 100 kPa abs, and 30°C. The duct is rectangular with cross-sectional dimensions of 1 m by 20 cm. What
Natural gas (methane) flows at 16 m/s through a pipe with a 1.5 m diameter. The temperature of the methane is 15°C, and the pressure is 200 kPa gage. Determine the mass flow rate.
A pipe whose diameter is 10 cm transports air with a temperature of 20°C and pressure of 253 kPa absolute at 50 m/s.Determine the mass flow rate.
A pipe with a 2 m diameter carries water having a velocity of 4 m/s. What is the discharge in cubic meters per second and in cubic feet per second?
A pipe with a 21 in. diameter carries water having a velocity of 10 ft /s. What is the discharge in cubic feet per second and in gallons per minute (1 cfs equals 449 gpm)?
The discharge of water in a 27-cm-diameter pipe is 0.057 m3/s. What is the mean velocity?
For flow of a gas in a pipe, which form of the continuity equation is more general?a. V1A1 = V2A2b. ρ1V1A1 = ρ2V2A2c. Both are equally applicable
A liquid flows through a pipe with a constant velocity. If a pipe twice the size is used with the same velocity, will the flow rate be (a) Halved, (b) Doubled, or(c) Quadrupled? Explain.
Another name for the volume flow rate equation could bea. The discharge equationb. The mass flow rate equationc. Either a or b
Taking a jar of known volume, fill with water from your household tap and measure the time to fill. Calculate the discharge from the tap. Estimate the cross-sectional area of the faucet outlet, and
The average flow rate (release) through Grand Coulee Dam is 110,000 ft3/s. The width of the river downstream of the dam is 100 yards. Making a reasonable estimate of the river velocity, estimate the
A closed cylindrical tank of water (ρ = 1000 kg/m3) is rotated about its horizontal axis as shown. The water inside the tank rotates with the tank (V = rω). Derive an equation for dp/dz along a
A simple centrifugal pump consists of a 10 cm disk with radial ports as shown. Water is pumped from a reservoir through a central tube on the axis. The wheel spins at 3000 rev/min, and the liquid
Water (ρ = 1000 kg/m3) stands in the closed-end U-tube as shown when there is no rotation. If ℓ = 2 cm and if the entire system is rotated about axis A-A, at what angular speed will water just
Water (ρ = 1000 kg/m3) fills a slender tube 1 cm in diameter, 40 cm long, and closed at one end. When the tube is rotated in the horizontal plane about its open end at a constant speed of 50 rad/s,
A fuel tank for a rocket in space under a zero-g environment is rotated to keep the fuel in one end of the tank. The system is rotated at 3 rev/min. The end of the tank (point A) is 1.5 m from the
A manometer is rotated around one leg, as shown. The difference in elevation between the liquid surfaces in the legs is 20 cm. The radius of the rotating arm is 10 cm. The liquid in the manometer is
An arm with a stagnation tube on the end is rotated at 100 rad/s in a horizontal plane 10 cm below a liquid surface as shown. The arm is 20 cm long, and the tube at the center of rotation extends
A U-tube is rotated about one leg, as shown. Before being rotated the liquid in the tube fills 0.25 m of each leg. The length of the base of the U-tube is 0.5 m, and each leg is 0.5 m long. What
A closed tank of liquid (SG = 1.2) is rotated about a vertical axis (see the fi gure), and at the same time the entire tank is accelerated upward at 4 m/s2. If the rate of rotation is 10 rad/s, what
Separators are used to separate liquids of different densities, such as cream from skim milk, by rotating the mixture at high speeds. In a cream separator, the skim milk goes to the outside while the
This closed tank, which is 4 ft in diameter, is filled with water (ρ = 62.4 lbm/ft 3) and is spun around its vertical axis at a rate of 10 rad/s. An open piezometer is connected to the tank as shown
Knowing the speed at point 1 of a fluid upstream of a sphere and the average speed at point 2 in the wake of in the sphere, can one use the Bernoulli equation to fi nd the pressure difference between
Figure 4.36 shows irrotational flow past a circular cylinder. Assume that the approach velocity at A is constant (does not vary with time).a. Is the flow past the cylinder steady or unsteady?b. Is
The pressure in the wake of a bluff body is approximately equal to the pressure at the point of separation. The velocity distribution for flow over a sphere is V = 1.5 V0 sin θ, where V0 is the
Consider the flow of water between two parallel plates in which one plate is fixed as shown. The distance between the plates is h, and the speed of the moving plate is V. A person wishes to calculate
Ideal flow theory will yield a flow pattern past an airfoil similar to that shown. If the approach air velocity V0 is 80 m/s, what is the pressure difference between the bottom and the top of this
Water (ρ = 62.4 lbm/ft 3) flows from the large orifice at the bottom of the tank as shown. Assume that the flow is irrotational. Point B is at zero elevation, and point A is at 1 ft elevation. If VA
The velocity and gage pressure are given at two points in the flow field. Assume that the two points lie in a horizontal plane and that the fluid density is uniform in the flow field and is equal to
The maximum velocity of the flow past a circular cylinder, as shown, is twice the approach velocity. What is Δp between the point of highest pressure and the point of lowest pressure in a 40 m/s
The velocity in the outlet pipe from this reservoir is 8 m/s and h = 19 m. Because of the rounded entrance to the pipe, the flow is assumed to be irrotational. Under these conditions, what is the
Th e velocity in the outlet pipe from this reservoir is 30 ft/s and h = 18 ft . Because of the rounded entrance to the pipe, the flow is assumed to be irrotational. Under these conditions, what is

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