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engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Estimate the discharge of water (T = 10°C) that flows 1.5 m deep in a long rectangular concrete channel that is 3 m wide and is on a slope of 0.001. Use the Darcy-Weisbach equation.
Consider channels of rectangular cross section carrying 100 cfs of water flow. The channels have a slope of 0.001. Determine the cross-sectional areas required for widths of 2 ft, 4 ft, 6 ft, 8 ft,
A concrete (assume n = 0.013) sewer pipe 2.5 ft in diameter is laid so it has a drop in elevation of 1.0 ft per 800 ft of length. If sewage (assume the properties are the same as those of water)
Determine the discharge in a 5 ft diameter smooth (troweled) concrete sewer pipe on a slope of 0.001 that is carrying water at a depth of 4 ft.
Water flows at a depth of 8 ft in the trapezoidal, concrete lined channel shown. If the channel slope is 1 ft in 1500 ft, what is the average velocity, and what is the discharge? Use the Darcy-
What will be the depth of flow in a trapezoidal troweled concrete-lined channel that has a water discharge of 1000 cfs? The channel has a slope of 1 ft in 500 ft. The bottom width of the channel is
What discharge of water will occur in a trapezoidal channel that has a bottom width of 18ft and side slopes of 1 vertical to 1 horizontal if the slope of the channel is 2ft/mile and the depth is 4ft?
A rectangular concrete channel 4 m wide on a slope of 0.004 is designed to carry a water (T = 10°C) discharge of 25 m3/s. Estimate the uniform flow depth for these conditions. The channel has a
A rectangular troweled concrete channel 8 ft wide with a slope of 10 ft in 3000 ft is designed for a discharge of 400 cfs. For a water temperature of 40°F, estimate the depth of flow.
A concrete-lined trapezoidal channel with a bottom width of 10 ft and side slopes of 1 vertical to 2 horizontal is designed to carry a flow of 3000 cfs. If the slope of the channel is 0.001, what
Design a canal with a trapezoidal cross section to carry a design discharge of irrigation water of 900 cfs. The slope of the canal is to be 0.002. The canal is to be lined with unfinished concrete,
How are head loss and slope related for nonuniform flow, as compared to uniform flow?
Is critical flow a desirable or undesirable flow condition? Why?
Critical flow _____. (Select all of the following that are correct.)a. Occurs when specific energy is a minimum for a given discharge.b. Occurs when the discharge is maximum for a given specific
Water flows at a depth of 100 in. with a velocity of 25 ft/s in a rectangular channel, with width = 3 ft.(a) Is the flow subcritical or supercritical? (b) What is the alternate depth?
The water discharge in a rectangular channel 20 ft wide is 550 cfs. If the depth of water is 3 ft , is the flow subcritical or supercritical?
The discharge in a rectangular channel 18 ft wide is 420 cfs. If the water velocity is 9 ft /s, is the flow subcritical or supercritical?
Water flows at a rate of 8 m3/s in a rectangular channel 2 m wide. Determine the Froude number and the type of flow (subcritical, critical, or supercritical) for depths of 30 cm, 1.0 m, and 2.0 m.
For a rectangular channel 3 m wide and discharge of 12 m3, what is the alternate depth to the 90 cm depth? What is the specific energy for these conditions?
Water flows at the critical depth with a velocity of 12 m/s. What is the depth of flow?
Water flows uniformly at a rate of 320 cfs in a rectangular channel that is 12 ft wide and has a bottom slope of 0.005. If n is 0.014, is the flow subcritical or supercritical?
The discharge in a trapezoidal channel is 10 m3/s. The bottom width of the channel is 3.0 m, and the side slopes are 1 vertical to 1 horizontal. If the depth of flow is 1.0m, is the flow
A rectangular channel is 6 m wide, and the discharge of water in it is 18 m3/s. Plot depth versus specific energy for these conditions. Let specific energy range from Emin to E = 7 m. What are the
A long rectangular channel that is 8 m wide and has a mild slope ends in a free outfall. If the water depth at the brink is 0.55 m, what is the discharge in the channel?
A broad-crested weir is used to measure discharge in an irrigation ditch. Calculate the discharge. The weir is 10 ft long, 4 ft high, and the head on the weir is 2.4 ft. Use Figure 15.13 to find the
What discharge of water will occur over a 2 m high, broadcrested weir that is 5 m long if the head on the weir is 60 cm?
The crest of a high, broad-crested weir has an elevation of 100 m. If the weir is 10 m long and the discharge of water over the weir is 25 m3/s, what is the water-surface elevation in the reservoir
The crest of a high, broad-crested weir has an elevation of 300 ft . If the weir is 40 ft long and the discharge of water over the weir is 1200 cfs, what is the water-surface elevation in the
Water flows with a velocity of 3 m/s and at a depth of 3 m in a rectangular channel. What is the change in depth and in water-surface elevation produced by a gradual upward change in bottom elevation
Water flows with a velocity of 2 m/s and at a depth of 3 m in a rectangular channel. What is the change in depth and in water-surface elevation produced by a gradual upward change in bottom elevation
Assuming no energy loss, what is the maximum value of Δz that will permit the unit flow rate of 6 m2/s to pass over the hump without increasing the upstream depth? Sketch carefully the water-surface
Water flows with a velocity of 3 m/s in a rectangular channel 3 m wide at a depth of 3 m. What is the change in depth and in water-surface elevation produced when a gradual contraction in the channel
A rectangular channel that is 10 ft wide is very smooth except for a small reach that is roughened with angle irons attached to the bottom. Water flows in the channel at a rate of 200 cfs and at a
Water flows from a reservoir into a steep rectangular channel that is 4 m wide. The reservoir water surface is 3 m above the channel bottom at the channel entrance. What discharge will occur in the
A small wave is produced in a pond that is 18 in. deep. What is the speed of the wave in the pond?
A small wave in a pool of water having constant depth travels at a speed of 3 m/s. How deep is the water?
As waves in the ocean approach a sloping beach, they curve so that they are nearly parallel to the beach when they finally break (see accompanying figure). Explain why the waves curve like this. With
For a hydraulic jump, __________. (Select all of the following that are correct.)a. The flow changes from subcritical to supercritical.b. The flow changes from supercritical to subcritical.c.
The baffled ramp shown is used as an energy dissipator in a two-dimensional open channel. For a discharge of 18 cfs per foot of width, calculate the head lost, the power dissipated, and the
The spillway shown has a discharge of 3.1 m3/s per meter of width occurring over it. What depth y2 will exist downstream of the hydraulic jump? Assume negligible energy loss over the spillway. y2 5 m
The flow of water downstream from a sluice gate in a horizontal channel has a depth of 35 cm and a flow rate of 7 m3/s per meter of width. The sluice gate is 2 m wide. a. Could a hydraulic jump
It is known that the discharge per unit width is 65 cfs/ft and that the height (H) of the hydraulic jump is 14 ft. What is the depth y1? H
Water flows in a channel at a depth of 40 cm and with a velocity of 8 m/s. An obstruction causes a hydraulic jump to be formed. What is the depth of flow downstream of the jump?
Water flows in a trapezoidal channel at a depth of 40 cm and with a velocity of 10 m/s. An obstruction causes a hydraulic jump to be formed. What is the depth of flow downstream of the jump? The
A hydraulic jump occurs in a wide rectangular channel. If the depths upstream and downstream are 0.50 ft and 10 ft, respectively, what is the discharge per foot of width of channel?
The 20 ft wide rectangular channel shown has three different reaches. S0,1 = 0.01; S0,2 = 0.0004; S0, = 0.00317; Q = 500 cfs; n1 = 0.015; normal depth for reach 2 is 5.4 ft and that for reach 3
Water flows from under the sluice gate as shown and continues on to a free overfall (also shown). Upstream from the overfall the flow soon reaches a normal depth of 1.1 m. The profile immediately
Water is flowing as shown under the sluice gate in a horizontal rectangular channel that is 5ft wide. The depths of y0 and y1 are 65ft and 1ft, respectively. What will be the horsepower lost in the
Water flows uniformly at a depth y1 = 32 cm in the concrete channel shown, which is 8 m wide. Estimate the height of the hydraulic jump that will form when a sill is installed to force it to form.
The normal depth in the channel downstream of the sluice gate shown is 1 m. What type of water-surface profile occurs downstream of the sluice gate? Also, estimate the shear stress on the smooth
Water flows at a rate of 100 ft3/s in a rectangular channel 10ft wide. The normal depth in that channel is 2ft. The actual depth of flow in the channel is 4ft. The water-surface profile in the
Th e water-surface profile labeled with a question mark is(a) M2, (b) S2, (c) H2, or (d) A2. Horizontal
The partial water-surface profile shown is for a rectangular channel that is 3 m wide and has water flowing in it at a rate of 5 m3/s. Sketch in the missing part of the water-surface profile and
A very long 10 ft wide concrete rectangular channel with a slope of 0.0001 ends with a free overfall. The discharge in the channel is 120 cfs. One mile upstream the flow is uniform. What kind
The discharge per foot of width in this rectangular channel is 20cfs. The normal depths for parts 1 and 3 are 0.5ft and 1.00ft , respectively. The slope for part 2 is 0.001 (sloping upward in the
Consider the hydraulic jump shown for the long horizontal rectangular channel. What kind of water-surface profile (classification) is located upstream of the jump? What kind of water-surface profile
The steep rectangular concrete spillway shown is 4 m wide and 500 m long. It conveys water from a reservoir and delivers it to a free outfall. The channel entrance is rounded and smooth (negligible
The concrete rectangular channel shown is 3.5 m wide and has a bottom slope of 0.001. The channel entrance is rounded and smooth (negligible head loss at the entrance), and the reservoir water
A dam 50 m high backs up water in a river valley as shown. During flood flow, the discharge per meter of width, q, is equal to 10 m2/s. Making the simplifying assumptions that R = y and f = 0.030,
Which of the following could be considered a model? Why? (Select all that apply.)a. The ideal gas lawb. A set of instructions for using a Pitot-static tube to measure velocityc. An airplane built
Apply the modeling building process to the following task. Your team is designing a helium-filled balloon that will travel to at least 80,000 feet elevation in the atmosphere. The balloon will
Apply the modeling building process to the following task. Your team is designing a two-stage, solid-fuel rocket that is intended to travel to 15,000 feet and then take photos. Right now, you choose
Why do you think that engineers make the effort to learn partial differential equations? What are the benefits to them?
Consider the function f (x) = ln(x). Show how to find the Taylor series expansion for the function f(x) about the point x = a. Then, find the numerical value for x = 1.5 and six terms of the Taylor
Consider a flat horizontal plate that is infinite in size in both dimensions. Above the plate is a fluid of viscosity μ. The plate is at rest. Then, at time equals zero seconds, the plate is set in
Compare and contrast the integral form of the continuity equation [(Eq. (5.28)] with the PDE form of the continuity equation [(Eq. (16.36)]. Address the following questions.a. Are the units and
Start with the conservation form of the continuity equation in Cartesian coordinates and derive the non-conservation form.
Start with the nonconservation form of the continuity equation in Cartesian coordinates and derive the conservation form.
Consider water draining out of round hole in the bottom of a round tank. Assume constant density and also assume that the water does not swirl. Then,a. Select the general form of the continuity
Answer each question that follows.a. Is Eq. (16.72) in conservation form or nonconservation form? Why?b. Is Eq. (16.72) in invariant form or coordinate-specific form? Why?
What are the physics of the gradient of the pressure field? What are the units? What are the dimensions?
What are the physics of the divergence of the shear stress tensor? What are the units? What are the dimensions?
Compare the Navier-Stokes equation to Euler’s equation.a. What are two important similarities?b. What are two important differences?
A liquid flows between parallel boundaries as shown above. The velocity distribution near the lower wall is given in the following table:a. If the viscosity of the liquid is 10–3 N∙s/m2, what is
Kinematic viscosity (select all that apply)a. Is another name for absolute viscosityb. Is viscosity/densityc. Is dimensionless because forces are canceled outd. Has dimensions of L2/Te. Is only used
A spherical soap bubble has an inside radius R, a film thickness t, and a surface tension σ. Derive a formula for the pressure within the bubble relative to the outside atmospheric pressure. What is
Which of the following is the formula for the gage pressure within a very small spherical droplet of water:(a) p = σ/d, (b) p = 4σ/d, (c) p = 8σ/d?
Surface tension (select all that apply)a. Only occurs at an interface, or surfaceb. Has dimensions of energy/areac. Has dimensions of force/aread. Has dimensions of force/lengthe. Depends on adhesion
One type of viscometer involves the use of a rotating cylinder inside a fixed cylinder. Th e gap between the cylinders must be very small to achieve a linear velocity distribution in the liquid.
Some instruments having angular motion are damped by means of a disk connected to the shaft . The disk, in turn, is immersed in a container of oil, as shown. Derive a formula for the damping torque
The device shown consists of a disk that is rotated by a shaft. The disk is positioned very close to a solid boundary. Between the disk and the boundary is viscous oil.a. If the disk is rotated at a
A laminar flow occurs between two horizontal parallel plates under a pressure gradient dp/ds (dp/ds is a constant and the sign of dp/ds is negative.). The upper plate moves left with a speed ut. The
The sliding plate viscometer shown below is used to measure the viscosity of a fluid. The top plate is moving to the right with a constant velocity of V = 22 m/s in response to a force of F = 1 N.
Two plates are separated by a 1/4 in. space. The lower plate is stationary; the upper plate moves at a velocity of 12 ft/s. Oil (SAE 10W-30, 150°F), which fills the space between the plates, has the
Suppose that glycerin is flowing (T = 20°C) and that the pressure gradient dp/dx is –1.2 kPa/m. What are the velocity and shear stress at a distance of 11 mm from the wall if the space B between
The velocity distribution for the flow of crude oil at 100°F (μ = 8 × 10–5 lbf∙s/ft2) between two walls is shown and is given by u = 100y(0.1 – y) ft/s, where y is measured in feet and the
The velocity distribution for water (20°C) near a wall is given by u = a(y/b)1/6, where a = 10 m/s, b = 2 mm, and y is the distance from the wall in mm. Determine the shear stress in the water at y
SAE 10W-30 oil with viscosity 1 × 10–4 lbf∙s/ft2 is used as a lubricant between two parts of a machine that slide past one another with a velocity difference of 4 ft/s. What spacing, in inches,
At a point in a flowing fluid, the shear stress is 3 × 10–4 psi, and the velocity gradient is 1 s–1.a. What is the viscosity in traditional units?b. Convert this viscosity to SI units.c. Is this
Which of these materials will flow (deform) with even a small shear stress applied?a. A Bingham plasticb. A Newtonian fluid
Common Newtonian fluids area. Toothpaste, catsup, and paintb. Water, oil, and mercuryc. All of the above
The no-slip conditiona. Only applies to ideal flowb. Only applies to rough surfacesc. Means velocity, V, is zero at the walld. Means velocity, V, is the velocity of the wall
For the velocity gradient dV/dya. The coordinate axis for dy is parallel to velocityb. The coordinate axis for dy is perpendicular to velocity
The term dV/dy, the velocity gradienta. Has dimensions of L/Tb. Has dimensions of T –1
Shear stress has dimensions ofa. Sorce/areab. Dimensionless
Calculate the pressure increase that must be applied to liquid water to reduce its volume by 3%.
A pressure of 4 × 106 N/m2 is applied to mass of water that initially filled a 4300 cm3 volume. Estimate its volume after the pressure is applied.
Th e bulk modulus of elasticity of ethyl alcohol is 1.06 × 109 Pa. For water, it is 2.15 × 109 Pa. Which of these liquids is easier to compress?a. Ethyl alcoholb. Water
Dimensions of the bulk modulus of elasticity area. The same as the dimensions of pressure/densityb. The same as the dimensions of pressure/volumec. The same as the dimensions of pressure
If you have a bulk modulus of elasticity that is a very large number, then a small change in pressure would causea. A very large change in volumeb. A very small change in volume

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