Questions and Answers of Fluid Mechanics

For each statement, choose whether the statement is true or false and discuss your answer briefly. These statements concern a laminar boundary layer on a flat plate (Fig. P10–73C).(a) At a given
A laminar boundary layer growing along a flat plate is sketched in Fig. P10–75C. Several velocity profiles and the boundary layer thickness δ(x) are also shown. Sketch several streamlines in this
What is a trip wire, and what is its purpose?
Discuss the implication of an inflection point in a boundary layer profile. Specifically, does the existence of an inflection point infer a favorable or adverse pressure gradient? Explain.
Compare flow separation for a laminar versus turbulent boundary layer. Specifically, which case is more resistant to flow separation? Why? Based on your answer, explain why golf balls have dimples.
In your own words, summarize the five steps of the boundary layer procedure.
In your own words, list at least three “red flags” to look out for when performing laminar boundary layer calculations.
Two definitions of displacement thickness are given in this chapter. Write both definitions in your own words. For the laminar boundary layer growing on a flat plate, which is larger—boundary layer
Explain the difference between a favorable and an adverse pressure gradient in a boundary layer. In which case does the pressure increase downstream? Why?
On a hot day (T = 30°C), a truck moves along the highway at 29.1 m/s. The flat side of the truck is treated as a simple, smooth flat–plate boundary layer, to first approximation. Estimate the
A boat moves through water (T = 40°F), at 26.0 mi/h. A flat portion of the boat hull is 2.4 ft long, and is treated as a simple smooth flat plate boundary layer, to first approximation. Is the
Air flows parallel to a speed limit sign along the highway at speed V = 8.5 m/s. The temperature of the air is 25°C, and the width W of the sign parallel to the flow direction (i.e., its length) is
Static pressure P is measured at two locations along the wall of a laminar boundary layer (Fig. P10–87). The measured pressures are P1 and P2, and the distance between the taps is small compared to
Consider two pressure taps along the wall of a laminar boundary layer as in Fig. P10–87. The fluid is air at 25°C, U1 = 10.3 m/s, and the static pressure P1 is 2.44 Pa greater than static pressure
Air flows through the test section of a small wind tunnel at speed V = 7.5 ft/s. The temperature of the air is 80°F, and the length of the wind tunnel test section is 1.5 ft. Assume that the
Consider the Blasius solution for a laminar flat plate boundary layer. The non dimensional slope at the wall is given by Eq. 8 of Example 10–10. Transform this result to physical variables, and
For the small wind tunnel of Prob. 10–86E, assume the flow remains laminar, and estimate the boundary layer thickness, the displacement thickness, and the momentum thickness of the boundary layer
Calculate the value of shape factor H for the limiting case of a boundary layer that is infinitesimally thin (Fig. P10–91). This value of H is the minimum possible value.FIGURE P10–91 U(x)
A laminar flow wind tunnel has a test section that is 30 cm in diameter and 80 cm in length. The air is at 20°C. At a uniform air speed of 2.0 m/s at the test section inlet, by how much will the
Repeat the calculation of Prob. 10–92, except for a test section of square rather than round cross section, with a 30 cm × 30 cm cross section and a length of 80 cm. Compare the result to that of
Air at 20°C flows at V = 8.5 m/s parallel to a flat plate (Fig. P10–94). The front of the plate is well rounded, and the plate is 40 cm long. The plate thickness is h = 0.75 cm, but because of
A small, axisymmetric, low-speed wind tunnel is built to calibrate hot wires. The diameter of the test section is 6.68 in, and its length is 10.0 in. The air is at 70°F. At a uniform air speed of
Air at 70°F flows parallel to a smooth, thin, flat plate at 15.5 ft/s. The plate is 10.6 ft long. Determine whether the boundary layer on the plate is most likely laminar, turbulent, or somewhere in
In order to avoid boundary layer interference, engineers design a “boundary layer scoop” to skim off the boundary layer in a large wind tunnel (Fig. P10–97). The scoop is constructed of thin
Air at 20°C flows at V = 80.0 m/s over a smooth flat plate of length L = 17.5 m. Plot the turbulent boundary layer profile in physical variables (u as a function of y) at x = L. Compare the profile
The streamwise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness δ is approximated by the simple linear expression, u = Uy/δ for y < δ,
For the linear approximation of Prob. 10–99, use the definition of local skin friction coefficient and the Kármán integral equation to generate an expression for δ/x. Compare your result to the
Compare shape factor H (defined in Eq. 10–95) for a laminar versus a turbulent boundary layer on a flat plate, assuming that the turbulent boundary layer is turbulent from the beginning of the
One dimension of a rectangular flat plate is twice the other. Air at uniform speed flows parallel to the plate, and a laminar boundary layer forms on both sides of the plate. Which orientation—long
Integrate Eq. 5 to obtain Eq. 6 of Example 10–14, showing all your work.Eq. 5 and eq. 6 d8 dx 72 Cf.x 14 72 14 -0.027(Re)-¹/7 (5)
Consider a turbulent boundary layer on a flat plate. Suppose only two things are known: Cf, x ≅ 0.059 · (Rex)–1/5 and θ ≅ 0.097δ. Use the Kármán integral equation to generate an expression
Air at 30°C flows at a uniform speed of 35.0 m/s along a smooth flat plate. Calculate the approximate x-location along the plate where the boundary layer begins the transition process toward
An aluminum canoe moves horizontally along the surface of a lake at 3.5 mi/h (Fig. P10–106E). The temperature of the lake water is 50°F. The bottom of the canoe is 20 ft long and is flat. Is the
For each statement, choose whether the statement is true or false, and discuss your answer briefly.(a) The velocity potential function can be defined for three dimensional flows.(b) The vorticity
In this chapter, we discuss solid body rotation (Fig. P10–108) as an example of an inviscid flow that is also rotational. The velocity components are ur = 0, uθ = ωr, and uz = 0. Compute the
Calculate the nine components of the viscous stress tensor in cylindrical coordinates (see Chap. 9) for the velocity field of Prob. 10–108. Discuss your results.Data from Problem 108In this
In this chapter, we discuss the line vortex (Fig. P10–110) as an example of an irrotational flow field. The velocity components are ur = 0, uθ = Γ/(2πr), and uz = 0. Compute the viscous term of
Calculate the nine components of the viscous stress tensor in cylindrical coordinates (see Chap. 9) for the velocity field of Prob. 10–110. Discuss.Data from Problem 110In this chapter, we discuss
Water falls down a vertical pipe by gravity alone. The flow between vertical locations z1 and z2 is fully developed, and velocity profiles at these two locations are sketched in Fig. P10–112. Since
Suppose the vertical pipe of Prob. 10–112 is now horizontal instead. In order to achieve the same volume flow rate as that of Prob. 10–112, we must supply a forced pressure gradient. Calculate
The Blasius boundary layer profile is an exact solution of the boundary layer equations for flow over a flat plate. However, the results are somewhat cumbersome to use, since the data appear in
The stream wise velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness δ is approximated by the sine wave profile of Prob. 10–114. Generate
For the sine wave approximation of Prob. 10–114, use the definition of local skin friction coefficient and the Kármán integral equation to generate an expression for δ/x. Compare your result to
If the fluid velocity is zero in a flow field, the Navier-Stokes equation becomes (a) VP- pg = 0 (b)P DV Dt (c) p DV (d) p = -√²+p+μ² Dt DV (e) p- + pg + μ²=0 - +² Dt + VP - pg = 0
Which choice is not a scaling parameter used to nondimensionalize the equations of motion?(a) Characteristic length, L (b) Characteristic speed, V(c) Characteristic viscosity, μ (d) Characteristic
Which choice is not a non-dimensional variable defined to nondimensionalize the equations of motion? (a) t = ft (b) x* (d) g* tool 8 (e) p* 7 L P Po (c) V* 11: V
Which dimensionless parameter does not appear in the nondimensionalized Navier-Stokes equation?(a) Reynolds number (b) Prandtl number(c) Strouhal number (d) Euler number (e) Froude number
Which dimensionless parameter is zero in the nondimensionalized Navier-Stokes equation when the flow is quasi-steady?(a) Euler number (b) Prandtl number (c) Froude number(d) Strouhal number (e)
If pressure P is replaced by modified pressure P´= P + ρgz in the nondimensionalized Navier-Stokes equation, which dimensionless parameter drops out?(a) Froude number (b) Reynolds number(c)
In creeping flow, the value of Reynolds number is typically(a) Re < 1 (b) Re ≪ 1 (c) Re > 1(d) Re ≫ 1 (e) Re = 0
Which equation is the proper approximate Navier- Stokes equation in dimensional form for creeping flow? (a) VP- pg = 0 (b)P + μ7² = 0 (c) -VP+ pg + ² = 0 DV (d) p Dt DV (e) p Dt +² + VP - pg = 0
For creeping flow over a three-dimensional object, the aerodynamic drag on the object does not depend on(a) Velocity, V (b) Fluid viscosity, μ (c) Characteristic length, L (d) Fluid density,
Consider a spherical ash particle of diameter 65 μm, falling from a volcano at a high elevation in air whose temperature is –50°C and whose pressure is 55 kPa. The density of air is 0.8588 kg/m3
Which statement is not correct regarding inviscid regions of flow?(a) Inertial forces are not negligible.(b) Pressure forces are not negligible.(c) Reynolds number is large.(d) Not valid in boundary
For which regions of flow is the Laplace equationapplicable?(a) Irrotational (b) Inviscid (c) Boundary layer(d) Wake (e) Creeping 0 = ФД
A very thin region of flow near a solid wall where viscous forces and rotationality cannot be ignored is called(a) Inviscid region of flow (b) Irrotational flow(c) Boundary layer (d) Outer flow
Which one of the following is not a flow region where the boundary layer approximation may be appropriate?(a) Jet (b) Inviscid region (c) Wake (d) Mixing layer(e) Thin region near a solid wall
Which statement is not correct regarding the boundary layer approximation?(a) The higher the Reynolds number, the thinner the boundary layer.(b) The boundary layer approximation may be appropriate
For a laminar boundary layer growing on a horizontal flat plate, the boundary layer thickness δ is not a function of(a) Velocity, V (b) Distance from the leading edge, x(c) Fluid density, ρ (d)
For flow along a flat plate with x being the distance from the leading edge, the boundary layer thickness grows like(a) x (b) √x (c) x2 (d) 1/x (e) 1/x2
Air flows at 25°C with a velocity of 3 m/s in a wind tunnel whose test section is 25 cm long. The displacement thickness at the end of the test section is (the kinematic viscosity of air is 1.562 ×
Air flows at 25°C with a velocity of 6 m/s over a flat plate whose length is 40 cm. The momentum thickness at the center of the plate is (the kinematic viscosity of air is 1.562 × 10–5 m2/s).(a)
Water flows at 20°C with a velocity of 1.1 m/s over a flat plate whose length is 15 cm. The boundary layer thickness at the end of the plate is (the density and viscosity of water are 998 kg/m3 and
Air flows at 15°C with a velocity of 12 m/s over a flat plate whose length is 80 cm. Using one-seventh power law of the turbulent flow, what is the boundary layer thickness at the end of the plate?
Explain why there is a significant velocity overshoot for the midrange values of the Reynolds number in the velocity profiles of Fig. 10–136, but not for the very small values of Re or for the very
Air at 15°C flows at 10 m/s over a flat plate of length 2 m. Using one-seventh power law of the turbulent flow, what is the ratio of local skin friction coefficient for the turbulent and laminar
Fairings are attached to the front and back of a cylindrical body to make it look more streamlined. What is the effect of this modification on the (a) Friction drag, (b) Pressure drag,(c) Total
The drag coefficient of a vehicle increases when its windows are rolled down or its sunroof is opened. A sports car has a frontal area of 18 ft2 and a drag coefficient of 0.32 when the windows and
One of the popular demonstrations in science museums involves the suspension of a ping-pong ball by an upward air jet. Children are amused by the ball always coming back to the center when it is
A tennis ball with a mass of 57 g and a diameter of 6.4 cm is hit with an initial velocity of 105 km/h and a backspin of 4200 rpm. Determine if the ball falls or rises under the combined effect of
Calculate the thickness of the boundary layer during flow over a 2.5-m-long flat plate at intervals of 25 cm and plot the boundary layer over the plate for the flow of (a) Air,(b) Water,(c) Engine
A small aluminum ball with D = 2 mm and ρs = 2700 kg/m3 is dropped into a large container filled with oil at 40°C (ρf = 876 kg/m3 and μ = 0.2177 kg/m·s). The Reynolds number is expected to be
Which quantities are physical phenomena associated with fluid flow over bodies?I. Drag force acting on automobilesII. The lift developed by airplane wingsIII. Upward draft of rain and snowIV. Power
The sum of the components of the pressure and wall shear forces in the direction normal to the flow is called(a) Drag (b) Friction(c) Lift (d) Bluff (e) Blunt
A car is moving at a speed of 70 km/h in air at 20°C. The frontal area of the car is 2.4 m2. If the drag force acting on the car in the flow direction is 205 N, the drag coefficient of the car is(a)
A person is driving his motorcycle at a speed of 110 km/h in air at 20°C. The frontal area of the motorcycle and driver is 0.75 m2. If the drag coefficient under these conditions is estimated to be
The manufacturer of a car reduces the drag coefficient of the car from 0.38 to 0.33 as a result of some modifications in its shape and design. If, on average, the aerodynamic drag accounts for 20
The region of flow trailing the body where the effects of the body are felt is called(a) Wake (b) Separated region (c) Stall(d) Vortice (e) Irrotational
The turbulent boundary layer can be considered to consist of four regions. Which choice is not one of them?(a) Buffer layer (b) Overlap layer (c) Transition layer(d) Viscous layer (e) Turbulent
Water at 10°C flows over a 1.1-m-long flat plate with a velocity of 0.55 m/s. If the width of the plate is 2.5 m, calculate the drag force acting on the top side of the plate. (Water properties at
Water at 10°C flows over a 3.75-m-long flat plate with a velocity of 1.15 m/s. If the width of the plate is 6.5 m, calculate the average friction coefficient over the entire plate. (Water properties
Air at 308C flows over a 3.0-cm-outer-diameter, 45-m-long pipe with a velocity of 6 m/s. Calculate the drag force exerted on the pipe by the air. (Air properties at 30°C are: ρ = 1.164 kg/m3, ν =
A 0.8-m-outer-diameter spherical tank is completely submerged in a flowing water stream at a velocity of 2.5 m/s. Calculate the drag force acting on the tank. (Water properties are: ρ = 998.0 kg/m3,
An airplane has a total mass of 18,000 kg and a wing planform area of 35 m2. The density of air at the ground is 1.2 kg/m3. The maximum lift coefficient is 3.48. The minimum safe speed for takeoff
An airplane has a total mass of 35,000 kg and a wing planform area of 65 m2. The airplane is cruising at 10,000 m altitude with a velocity of 1100 km/h. The density of air on cruising altitude is
An airplane is cruising at a velocity of 800 km/h in air whose density is 0.526 kg/m3. The airplane has a wing planform area of 90 m2. The lift and drag coefficients on cruising conditions are
Write a report on the history of the reduction of the drag coefficients of cars and obtain the drag coefficient data for some recent car models from the catalogs of car manufacturers or from the
Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain.
What is the effect of friction on flow velocity in subsonic Fanno flow? Answer the same question for supersonic Fanno flow.
On a T-s diagram of Fanno flow, what do the points on the Fanno line represent?
What is the effect of friction on the entropy of the fluid during Fanno flow?
Consider supersonic Fanno flow that is decelerated to sonic velocity (Ma = 1) at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct
Consider supersonic Fanno flow of air with an inlet Mach number of 1.8. If the Mach number decreases to 1.2 at the duct exit as a result of friction, does the (a) Stagnation temperature T0, (b)
What is the characteristic aspect of Fanno flow? What are the main approximations associated with Fanno flow?
Consider subsonic Fanno flow accelerated to sonic velocity (Ma = 1) at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct exit be
Consider subsonic Fanno flow of air with an inlet Mach number of 0.70. If the Mach number increases to 0.90 at the duct exit as a result of friction, will the (a) Stagnation temperature T0, (b)
Air enters a 12-cm-diameter adiabatic duct at Ma1 = 0.4, T1 = 550 K, and P1 = 200 kPa. The average friction factor for the duct is estimated to be 0.021. If the Mach number at the duct exit is 0.8,
Air enters a 15-m-long, 4-cm-diameter adiabatic duct at V1 = 70 m/s, T1 = 500 K, and P1 = 300 kPa. The average friction factor for the duct is estimated to be 0.023. Determine the Mach number at the
Air enters a 5-cm-diameter, 4-m-long adiabatic duct with inlet conditions of Ma1 = 2.8, T1 = 380 K, and P1 = 80 kPa. It is observed that a normal shock occurs at a location 3 m from the inlet. Taking
Helium gas with k = 1.667 enters a 6-in-diameter duct at Ma1 = 0.2, P1 = 60 psia, and T1 = 600 R. For an average friction factor of 0.025, determine the maximum duct length that will not cause the

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