Questions and Answers of Fluid Mechanics

Air enters a 15-cm-diameter adiabatic duct with inlet conditions of V1 = 150 m/s, T1 = 500 K, and P1 = 200 kPa. For an average friction factor of 0.014, determine the duct length from the inlet where
Air flows through a 6-in-diameter, 50-ft-long adiabatic duct with inlet conditions of V1 = 500 ft/s, T01 = 650 R, and P1 = 50 psia. For an average friction factor of 0.02, determine the velocity,
Consider subsonic airflow through a 20-cmdiameter adiabatic duct with inlet conditions of T1 = 330 K, P1 = 180 kPa, and Ma1 = 0.1. Taking the average friction factor to be 0.02, determine the duct
Argon gas with k = 1.667, cp = 0.5203 kJ/kg·K, and R = 0.2081 kJ/kg·K enters an 8-cmdiameter adiabatic duct with V1 = 70 m/s, T1 = 520 K, and P1 = 350 kPa. Taking the average friction factor to be
Air in a room at T0 = 300 K and P0 = 100 kPa is drawn steadily by a vacuum pump through a 1.4-cm-diameter, 35-cm-long adiabatic tube equipped with a converging nozzle at the inlet. The flow in the
Repeat Prob. 12–114 for a friction factor of 0.025 and a tube length of 1 m.Data from Prob. 12–114Air in a room at T0 = 300 K and P0 = 100 kPa is drawn steadily by a vacuum pump through a
Air in a room at T0 = 290 K and P0 = 90 kPa is to be drawn by a vacuum pump through a 3-cm-diameter, 2-m-long adiabatic tube equipped with a converging nozzle at the inlet. The flow in the nozzle
Air enters a 5.5-cm-diameter adiabatic duct with inlet conditions of Ma1 = 2.2, T1 = 250 K, and P1 = 70 kPa, and exits at a Mach number of Ma2 = 1.8. Taking the average friction factor to be 0.03,
Consider supersonic airflow through a 12-cmdiameter adiabatic duct with inlet conditions of T1 = 500 K, P1 = 80 kPa, and Ma1 = 3. Taking the average friction factor to be 0.03, determine the duct
Combustion gases with an average specific heat ratio of k = 1.33 and a gas constant of R = 0.280 kJ/kg·K enter a 10-cm-diameter adiabatic duct with inlet conditions of Ma1 = 2, T1 = 510 K, and P1 =
Air is flowing through a 6-cm-diameter adiabatic duct with inlet conditions of V1 = 120 m/s, T1 = 400 K, and P1 5 100 kPa and an exit Mach number of Ma2 = 1. To study the effect of duct length on the
Design a 1-m-long cylindrical wind tunnel whose diameter is 25 cm operating at a Mach number of 1.8. Atmospheric air enters the wind tunnel through a converging–diverging nozzle where it is
A one-third scale model of an airplane is to be tested in water. The airplane has a velocity of 900 km/h in air at –50°C. The water temperature in the test section is 10°C.The properties of air
A one-fourth scale model of an airplane is to be tested in water. The airplane has a velocity of 700 km/h in air at −50°C. The water temperature in the test section is 10°C.In order to achieve
A one-fourth scale model of a car is to be tested in a wind tunnel. The conditions of the actual car are V = 45 km/h and T = 0°C and the air temperature in the wind tunnel is 20°C. In order to
Consider the flow of oil with ρ = 894 kg/m3 and μ = 2.33 kg/m·s in a 28-cm-diameter pipeline at an average velocity of 0.5 m/s. A 330-m-long section of the pipeline passes through the icy waters
What is the generally accepted value of the Reynolds number above which the flow in smooth pipes is turbulent?
Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness δ, downstream distance x, freestream velocity V, fluid density ρ,
Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness δ, downstream distance x, free-stream velocity V, fluid density
Consider unsteady fully developed Coutte flow-flow between two infinite parallel plates. This problem involves the following parameters: velocity component u, distance between the plates h, vertical
Consider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness δ, downstream distance x, freestream velocity V, fluid density ρ,
What is the difference between the operating principles of thermal and laser Doppler anemometers?
A clothes dryer discharges air at 1 atm and 120°F at a rate of 1.2 ft3/s when its 5-in-diameter, well-rounded vent with negligible loss is not connected to any duct. Determine the flow rate when the
Oil at 20°C is flowing through a vertical glass funnel that consists of a 20-cm-high cylindrical reservoir and a 1-cm-diameter, 40-cm-high pipe. The funnel is always maintained full by the addition
Repeat Prob. 8–84 assuming (a) The diameter of the pipe is tripled (b) The length of the pipe is tripled while the diameter is maintained the same.Data from Problem 8–84Oil at 20°C is flowing
What is the difference between laser Doppler velocimetry (LDV) and particle image velocimetry (PIV)?
What are the primary considerations when selecting a flowmeter to measure the flow rate of a fluid?
Explain how flow rate is measured with a Pitotstatic tube, and discuss its advantages and disadvantages with respect to cost, pressure drop, reliability, and accuracy.
Explain how flow rate is measured with obstruction- type flowmeters. Compare orifice meters, flow nozzles, and Venturi meters with respect to cost, size, head loss, and accuracy.
How do positive displacement flowmeters operate? Why are they commonly used to meter gasoline, water, and natural gas?
Explain how flow rate is measured with a turbine flowmeter, and discuss how they compare to other types of flowmeters with respect to cost, head loss, and accuracy.
The head loss for a certain circular pipe is given by where f is the friction factor (dimensionless), L is the pipe length, V̇ is the volumetric flow rate, and D is the pipe diameter. Determine if
A Venturi meter equipped with a differential pressure gage is used to measure the flow rate of water at 15°C (ρ = 999.1 kg/m3) through a 5-cm-diameter horizontal pipe. The diameter of the Venturi
The mass flow rate of air at 20°C (ρ = 1.204 kg/m3) through a 18-cm-diameter duct is measured with a Venturi meter equipped with a water manometer. The Venturi neck has a diameter of 5 cm, and the
A flow nozzle equipped with a differential pressure gage is used to measure the flow rate of water at 10°C (ρ = 999.7 kg/m3 and μ = 1.307 × 10–3 kg/m·s) through a 3-cm-diameter horizontal
A 22-L kerosene tank (ρ = 820 kg/m3) is filled with a 2-cm-diameter hose equipped with a 1.5-cm-diameter nozzle meter. If it takes 20 s to fill the tank, determine the pressure difference indicated
The flow rate of ammonia at 10°C (ρ = 624.6 kg/m3 and μ = 1.697 × 10–4 kg/m·s) through a 2-cm-diameter pipe is to be measured with a 1.5-cm-diameter flow nozzle equipped with a differential
Consider flow from a reservoir through a horizontal pipe of length L and diameter D that penetrates into the side wall at a vertical distance H from the free surface. The flow rate through an actual
An elderly woman is rushed to the hospital because she is having a heart attack. The emergency room doctor informs her that she needs immediate coronary artery (a vessel that wraps around the heart)
A system that consists of two interconnected cylindrical tanks with D1 = 30 cm and D2 = 12 cm is to be used to determine the discharge coefficient of a short D0 = 5 mm diameter orifice. At the
Reconsider Prob. 8–150. In order to reduce the head losses in the piping and thus the power wasted, someone suggests doubling the diameter of the 83-m-long compressed air pipes. Calculating the
The compressed air requirements of a textile factory are met by a large compressor that draws in 0.6 m3/s air at atmospheric conditions of 20°C and 1 bar (100 kPa) and consumes 300 kW electric power
The average velocity for fully developed laminar pipe flow is(a) Vmax/2 (b) Vmax/3 (c) Vmax(d) 2Vmax/3 (e) 3Vmax/4
The Reynolds number is not a function of(a) Fluid velocity (b) Fluid density(c) Characteristic length (d) Surface roughness(e) Fluid viscosity
Air flows in a 5 cm by 8 cm cross section rectangular duct at a velocity of 4 m/s at 1 atm and 15°C. The Reynolds number for this flow is(a) 13,605 (b) 16,745 (c) 17,690 (d) 21,770(e) 23,235
Engine oil at 40°C (ρ = 876 kg/m3, μ = 0.2177 kg/m∙s) flows in a 20-cm-diameter pipe at a velocity of 1.2 m/s. The pressure drop of oil for a pipe length of 20 m is(a) 4180 Pa (b) 5044 Pa (c)
Consider laminar flow of water in a 0.8-cm-diameter pipe at a rate of 1.15 L/min. The velocity of water halfway between the surface and the center of the pipe is(a) 0.381 m/s (b) 0.762 m/s (c) 1.15
Air at 1 atm and 208C flows in a 4-cm-diameter tube. The maximum velocity of air to keep the flow laminar is(a) 0.872 m/s (b) 1.52 m/s (c) 2.14 m/s(d) 3.11 m/s (e) 3.79 m/s
Consider laminar flow of water at 158C in a 0.7-cmdiameter pipe at a velocity of 0.4 m/s. The pressure drop of water for a pipe length of 50 m is(a) 6.8 kPa (b) 8.7 kPa (c) 11.5 kPa (d) 14.9
A fluid flows in a 25-cm-diameter pipe at a velocity of 4.5 m/s. If the pressure drop along the pipe is estimated to be 6400 Pa, the required pumping power to overcome this pressure drop is(a) 452
Water flows in a 15-cm-diameter pipe at a velocity of 1.8 m/s. If the head loss along the pipe is estimated to be 16 m, the required pumping power to overcome this head loss is(a) 3.22 kW (b) 3.77
Air at 1 atm and 40°C flows in a 8-cm-diameter pipe at a rate of 2500 L/min. The friction factor is determined from the Moody chart to be 0.027. The required power input to overcome the pressure
Air at 1 atm and 258C (v = 1.562 × 10–5 m2/s) flows in a 9-cm-diameter cast iron pipe at a velocity of 5 m/s. The roughness of the pipe is 0.26 mm. The head loss for a pipe length of 24 m is(a)
Consider air flow in a 10-cm-diameter pipe at a high velocity so that the Reynolds number is very large. The roughness of the pipe is 0.002 mm. The friction factor for this flow is(a) 0.0311 (b)
The pressure drop for a given flow is determined to be 100 Pa. For the same flow rate, if we reduce the diameter of the pipe by half, the pressure drop will be(a) 25 Pa (b) 50 Pa (c) 200 Pa (d)
Water at 10°C (ρ = 999.7 kg/m3, μ = 1.307 × 10–3 kg/m∙s) is to be transported in a 5-cm-diamater, 30-m-long circular pipe. The roughness of the pipe is 0.22 mm. If the pressure drop in the
The valve in a piping system causes a 3.1 m head loss. If the velocity of the flow is 6 m/s, the loss coefficient of this valve is(a) 0.87 (b) 1.69 (c) 1.25 (d) 0.54 (e) 2.03
A water flow system involves a 180° return bend (threaded) and a 90° miter bend (without vanes). The velocity of water is 1.2 m/s. The minor losses due to these bends are equivalent to a pressure
Consider a sharp-edged pipe exit for fully developed laminar flow of a fluid. The velocity of the flow is 4 m/s. This minor loss is equivalent to a head loss of(a) 0.72 m (b) 1.16 m (c) 1.63 m (d)
A constant-diameter piping system involves multiple flow restrictions with a total loss coefficient of 4.4. The friction factor of piping is 0.025 and the diameter of the pipe is 7 cm. These minor
Air flows in an 8-cm-diameter, 33-m-long pipe at a velocity of 5.5 m/s. The piping system involves multiple flow restrictions with a total minor loss coefficient of 2.6. The friction factor of pipe
Consider a pipe that branches out into two parallel pipes and then rejoins at a junction downstream. The two parallel pipes have the same lengths and friction factors. The diameters of the pipes are
Consider a pipe that branches out into two parallel pipes and then rejoins at a junction downstream. The two parallel pipes have the same lengths and friction factors. The diameters of the pipes are
A pump moves water from a reservoir to another reservoir through a piping system at a rate of 0.15 m3/min. Both reservoirs are open to the atmosphere. The elevation difference between the two
Consider a pipe that branches out into three parallel pipes and then rejoins at a junction downstream. All three pipes have the same diameters (D = 3 cm) and friction factors (f = 0.018). The lengths
The divergence theorem iswhere G(vector) is a vector, V is a volume, and A is the surface area that encloses and defines the volume. Express the divergence theorem in words. JV F-G dv du = & G-ñ
Explain the fundamental differences between a flow domain and a control volume.
What does it mean when we say that two or more differential equations are coupled?
For a three-dimensional, unsteady, incompressible flow field in which temperature variations are insignificant, how many unknowns are there? List the equations required to solve for these unknowns.
For an unsteady, compressible flow field that is two-dimensional in the x-y plane and in which temperature and density variations are significant, how many unknowns are there? List the equations
For an unsteady, incompressible flow field that is two-dimensional in the x-y plane and in which temperature variations are insignificant, how many unknowns are there? List the equations required to
A Taylor series expansion of function f(x) about some x-location x0 is given asConsider the function f(x) = exp(x) = ex. Suppose we know the value of f(x) at x = x0, i.e., we know the value of f(x0),
Transform the position x(vector) = (2, 4, –1) from Cartesian (x, y, z) coordinates to cylindrical (r, θ, z) coordinates, including units. The values of x(vector) are in units of meters.
Transform the position x(vector) = (5 m, π/3 radians, 1.27 m) from cylindrical (r, θ, z) coordinates to Cartesian (x, y, z) coordinates, including units. Write all three components of x(vector) in
Let vector G(vector) be given byCalculate the divergence of G(vector), and simplify as much as possible. Is there anything special about your result? G = 2xzi - x²j-zk.
The outer product of two vectors is a second-order tensor with nine components. In Cartesian coordinates, it isThe product rule applied to the divergence of the product of two vectors F(vector) and
Use the product rule of Prob. 9–11 to show thatData from Problem 11The outer product of two vectors is a second-order tensor with nine components. In Cartesian coordinates, it isThe product rule
On many occasions we need to transform a velocity from Cartesian (x, y, z) coordinates to cylindrical (r, θ, z) coordinates (or vice versa). Using Fig. P9–13 as a guide, transform cylindrical
Using Fig. P9–13 as a guide, transform Cartesian velocity components (u, v, w) into cylindrical velocity components (ur, uθ, uz).FIGURE P9–13 y up V u 1 1 U₁
Beth is studying a rotating flow in a wind tunnel. She measures the u and v components of velocity using a hot-wire anemometer. At x = 0.40 m and y = 0.20 m, u = 10.3 m/s and v = –5.6 m/s.
Consider a spiraling line vortex/sink flow in the xy-or rθ-plane as sketched in Fig. P9–17. The two-dimensional cylindrical velocity components (ur, uθ) for this flow field are ur = C/2πr and
A steady, two-dimensional, incompressible velocity field has Cartesian velocity components u = Cy/(x2 + y2) and v = –Cx/(x2 + y2), where C is a constant. Transform these Cartesian velocity
Alex is measuring the time-averaged velocity components in a pump using a laser Doppler velocimeter (LDV). Since the laser beams are aligned with the radial and tangential directions of the pump, he
Let vector G(vector) be given byand let V be the volume of a cube of unit length with its corner at the origin, bounded by x = 0 to 1, y = 0 to 1, and z = 0 to 1 (Fig. P9–19). Area A is the surface
The product rule can be applied to the divergence of scalar f times vectorExpand both sides of this equation in Cartesian coordinates and verify that it is correct. Gas: V.(fG) = GVƒ+ ƒV. G.
In this chapter we derive the continuity equation in two ways: by using the divergence theorem and by summing mass flow rates through each face of an infinitesimal control volume. Explain why the
If a flow field is compressible, what can we say about the material derivative of density? What about if the flow field is incompressible?
A Pitot-static probe is mounted in a 2.5-cm-inner diameter pipe at a location where the local velocity is approximately equal to the average velocity. The oil in the pipe has density ρ = 860 kg/m3
Calculate the Reynolds number of the flow of Prob. 8–114. Is it laminar or turbulent?Data from Problem 8–114A Pitot-static probe is mounted in a 2.5-cm-inner diameter pipe at a location where the
The flow rate of water through a 10-cm-diameter pipe is to be determined by measuring the water velocity at several locations along a cross section. For the set of measurements given in the table,
An orifice with a 1.8-in-diameter opening is used to measure the mass flow rate of water at 60°F (ρ = 62.36 lbm/ft3 and μ = 7.536 × 10–4 lbm/ft·s) through a horizontal 4-in-diameter pipe. A
Repeat Prob. 8–118E for a differential height of 10 in.Data from Problem 8–118EAn orifice with a 1.8-in-diameter opening is used to measure the mass flow rate of water at 60°F (ρ = 62.36
Air (ρ = 1.225 kg/m3 and μ = 1.789 × 10–5 kg/m·s) flows in a wind tunnel, and the wind tunnel speed is measured with a Pitot-static probe. For a certain run, the stagnation pressure is measured
Reconsider Prob. 8–121. Letting the pressure drop vary from 1 kPa to 10 kPa, evaluate the flow rate at intervals of 1 kPa, and plot it against the pressure drop.Data from Problem 8–121A Venturi
Repeat Prob. 8–123 for a Venturi neck diameter of 6 cm.Data from Problem 8–123The mass flow rate of air at 20°C (ρ = 1.204 kg/m3) through a 18-cm-diameter duct is measured with a Venturi meter
A vertical Venturi meter equipped with a differential pressure gage shown in Fig. P8–125 is used to measure the flow rate of liquid propane at 10°C (ρ = 514.7 kg/m3) through an 10-cm-diameter
The volume flow rate of liquid refrigerant-134a at 10°F (ρ = 83.31 lbm/ft3) is to be measured with a horizontal Venturi meter with a diameter of 5 in at the inlet and 2 in at the throat. If a
The flow rate of water at 20°C (ρ = 998 kg/m3 and μ = 1.002 × 10–3 kg/m · s) through a 4-cm-diameter pipe is measured with a 2-cm-diameter nozzle meter equipped with an inverted air–water
The conical container with a thin horizontal tube attached at the bottom, shown in Fig. P8–131, is to be used to measure the viscosity of an oil. The flow through the tube is laminar. The discharge
Oil at 20°C is flowing steadily through a 5-cmdiameter 40-m-long pipe. The pressures at the pipe inlet and outlet are measured to be 745 and 97.0 kPa, respectively, and the flow is expected to be

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