Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
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Textbook Question
Chapter 12, Problem 71P
Air at 0°C is contained in a large tank on the space shuttle. A converging section with exit area 1 × 10−3 m2 is attached to the tank, through which the air exits to space at a rate of 2 kg/s. What are the pressure in the tank, and the pressure, temperature, and speed at the exit?
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2. Consider a polymeric membrane within a 6 cm diameter stirred ultrafiltration cell. The membrane is
30 μm thick. The membrane has pores equivalent in size to a spherical molecule with a molecular weight
of 100,000, a porosity of 80%, and a tortuosity of 2.5. On the feed side of the membrane, we have a
solution containing a protein at a concentration of 8 g L-1 with these properties: a = 3 nm and DAB = 6.0 ×
10-7 cm² s¹. The solution viscosity is 1 cP. The hydrodynamic pressure on the protein side of the
membrane is 20 pounds per square inch (psi) higher than on the filtrate side of the membrane. Assume
that the hydrodynamic pressure difference is much larger than the osmotic pressure difference
(advection >> diffusion). Determine the convective flow rate of the solution across the membrane.
1. Calculate the filtration flow rate (cm³ s¹) of a pure fluid across a 100 cm² membrane. Assume the
viscosity (µ) of the fluid is 1.8 cP. The porosity of the membrane is 40% and the thickness of the
membrane is 500 μm. The pores run straight through the membrane and these pores have a radius of
0.225 μm. The pressure drop applied across the membrane is 75 psi. (Note: 1 cP = 0.001 N s m²² = 0.001
Pa s.)
3. Tong and Anderson (1996) obtained for BSA the following data in a polyacrylamide gel for the
partition coefficient (K) as a function of the gel volume fraction (4). The BSA they used had a molecular
weight of 67,000, a molecular radius of 3.6 nm, and a diffusivity of 6 × 10-7 cm2 s-1. Compare the
Ogston equation
K=exp
+
to their data and obtain an estimate for the radius of the cylindrical fibers (af) that comprise the gel.
Hint: You will need to plot Ink as a function of gel volume fraction as part of your analysis. Please include
your MATLAB, or other, code with your solution.
Gel Volume Fraction (4)
KBSA
0.00
1.0
0.025
0.35
0.05
0.09
0.06
0.05
0.075
0.017
0.085
0.02
0.105
0.03
Chapter 12 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 12 - Air is expanded in a steady flow process through a...Ch. 12 - Five kilograms of air is cooled in a closed tank...Ch. 12 - Air is contained in a piston-cylinder device. The...Ch. 12 - Calculate the power delivered by the turbine per...Ch. 12 - If hydrogen flows as a perfect gas without...Ch. 12 - A 1-m3 tank contains air at 0.1 MPa absolute and...Ch. 12 - Air enters a turbine in steady flow at 0.5 kg/s...Ch. 12 - Natural gas, with the thermodynamic properties of...Ch. 12 - Carbon dioxide flows at a speed of 10 m/s in a...Ch. 12 - In an isothermal process, 0.1 cubic feet of...
Ch. 12 - Calculate the speed of sound at 20C for (a)...Ch. 12 - An airplane flies at 550 km/hr at 1500 m altitude...Ch. 12 - Actual performance characteristics of the Lockheed...Ch. 12 - For a speed of sound in steel of 4300 m/s,...Ch. 12 - Determine and plot the Mach number of an...Ch. 12 - Investigate the effect of altitude on Mach number...Ch. 12 - The grandstand at the Kennedy Space Center is...Ch. 12 - Use data for specific volume to calculate and plot...Ch. 12 - An object traveling in atmospheric air emits two...Ch. 12 - An object traveling in atmospheric air emits two...Ch. 12 - While at the seashore, you observe an airplane...Ch. 12 - The temperature varies linearly from sea level to...Ch. 12 - Prob. 23PCh. 12 - A photograph of a bullet shows a Mach angle of 32....Ch. 12 - An F-4 aircraft makes a high-speed pass over an...Ch. 12 - All aircraft passes overhead at 3 km altitude. The...Ch. 12 - A supersonic aircraft flies at 3 km altitude at a...Ch. 12 - For the conditions of Problem 12.27, find the...Ch. 12 - The Concorde supersonic transport cruised at M =...Ch. 12 - Plot the percentage discrepancy between the...Ch. 12 - Compute the air density in the undisturbed air and...Ch. 12 - Carbon dioxide flows in a duct at a velocity of 90...Ch. 12 - If nitrogen at 15C is flowing and the stagnation...Ch. 12 - An aircraft cruises at M = 0.65 at 10 km altitude...Ch. 12 - High-speed aircraft use air data computers to...Ch. 12 - A supersonic wind tunnel test section is designed...Ch. 12 - Oxygen flows in a passage at a pressure of 25...Ch. 12 - What is the pressure on the nose of a bullet...Ch. 12 - Prob. 39PCh. 12 - Air flows in an insulated duct. At point the...Ch. 12 - Consider steady, adiabatic flow of air through a...Ch. 12 - Air passes through a normal shock in a supersonic...Ch. 12 - A Boeing 747 cruises at M = 0:87 at an altitude of...Ch. 12 - Space debris impact is a real concern for...Ch. 12 - A CO2 cartridge is used to propel a toy rocket....Ch. 12 - Nitrogen flows from a large tank, through a...Ch. 12 - Air flows from the atmosphere into an evacuated...Ch. 12 - Oxygen discharges from a tank through a convergent...Ch. 12 - The hot gas stream at the turbine inlet of a JT9-D...Ch. 12 - Carbon dioxide discharges from a tank through a...Ch. 12 - Air at 100F and 100 psia in a large tank flows...Ch. 12 - Calculate the required diameter of a convergent...Ch. 12 - Steam flows steadily and isentropically through a...Ch. 12 - Nitrogen flows through a diverging section of duct...Ch. 12 - At a section in a passage, the pressure is 30...Ch. 12 - In a given duct flow M = 2.0; the velocity...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Five pounds of air per second discharge from a...Ch. 12 - Air flows isentropically through a...Ch. 12 - Air, at an absolute pressure of 60.0 kPa and 27C,...Ch. 12 - Carbon dioxide flows from a tank through a...Ch. 12 - A convergent-divergent nozzle of 50-mm tip...Ch. 12 - Air flows adiabatically through a duct. At the...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Atmospheric air at 98.5 kPa and 20C is drawn into...Ch. 12 - The exit section of a convergent-divergent nozzle...Ch. 12 - Air flowing isentropically through a converging...Ch. 12 - Air flows from a large tank at p = 650 kPa...Ch. 12 - A converging nozzle is connected to a large tank...Ch. 12 - Air at 0C is contained in a large tank on the...Ch. 12 - A large tank initially is evacuated to 10 kPa...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Air enters a converging-diverging nozzle at 2 MPa...Ch. 12 - Prob. 75PCh. 12 - A jet transport aircraft, with pressurized cabin,...Ch. 12 - A converging-diverging nozzle, with a throat area...Ch. 12 - Air, at a stagnation pressure of 7.20 MPa absolute...Ch. 12 - A small rocket motor, fueled with hydrogen and...Ch. 12 - Testing of a demolition explosion is to be...Ch. 12 - A total-pressure probe is placed in a supersonic...Ch. 12 - Air flows steadily through a long, insulated...Ch. 12 - Air discharges through a convergent-divergent...Ch. 12 - A normal shock wave exists in an airflow. The...Ch. 12 - Air approaches a normal shock at V1 = 900 m/s, p1...Ch. 12 - Air approaches a normal shock at M1 = 2.5, with...Ch. 12 - Air undergoes a normal shock. Upstream, T1 = 35C,...Ch. 12 - If, through a normal shock wave in air, the...Ch. 12 - The stagnation temperature in an airflow is 149C...Ch. 12 - A supersonic aircraft cruises at M = 2.2 at 12 km...Ch. 12 - The Concorde supersonic transport flew at M = 2.2...
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