Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
8th Edition
ISBN: 9781119080701
Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
Publisher: WILEY
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Chapter 3.6, Problem 109P
To determine
The pressure at section (3)
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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 3 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Ch. 3.2 - Prob. 1PCh. 3.2 - Air flows steadily along a streamline from point...Ch. 3.2 - Water flows steadily through the variable area...Ch. 3.2 - What pressure gradient along the streamline,...Ch. 3.2 - At a given location the airspeed is 20 m/s and the...Ch. 3.2 - What pressure gradient along the streamline,...Ch. 3.2 - The Bernoulli equation is valid for steady,...Ch. 3.2 - An incompressible fluid flows steadily past a...Ch. 3.2 - Consider a compressible liquid that has a constant...Ch. 3.3 - Air flows along a horizontal, curved streamline...
Ch. 3.3 - Water flows around the vertical two-dimensional...Ch. 3.3 - Water in a container and air in a tornado flow in...Ch. 3.3 - Prob. 15PCh. 3.5 - At a given point on a horizontal streamline in...Ch. 3.5 - A drop of water in a zero-g environment (as in the...Ch. 3.5 - When an airplane is flying 200 mph at 5000-ft...Ch. 3.5 - Air flows over the airfoil shown in Fig. P3.20....Ch. 3.5 - Some animals have learned to take advantage of the...Ch. 3.5 - Estimate the pressure on your hand when you hold...Ch. 3.5 - 2013 Indianapolis 500 champion Tony Kanaan holds...Ch. 3.5 - What is the minimum height for an oil (SG = 0.75)...Ch. 3.5 - Prob. 25PCh. 3.5 - A Bourdon-type pressure gage is used to measure...Ch. 3.5 - Estimate the force of a hurricane strength wind...Ch. 3.5 - A 40-mph wind blowing past your house speeds up as...Ch. 3.5 - Prob. 29PCh. 3.6 - Prob. 30PCh. 3.6 - Estimate the pressure needed at the pumper truck...Ch. 3.6 - The tank shown in Fig. P3.32 contains air at...Ch. 3.6 - Water flows from the faucet on the first floor of...Ch. 3.6 - Prob. 34PCh. 3.6 - Prob. 35PCh. 3.6 - Streams of water from two tanks impinge upon each...Ch. 3.6 - Several holes are punched into a tin can as shown...Ch. 3.6 - Water flows from a pressurized tank, through a...Ch. 3.6 - Prob. 39PCh. 3.6 - Prob. 41PCh. 3.6 - Figure P3.42 shows a tube for siphoning water from...Ch. 3.6 - For the pipe enlargement shown in Fig. P3.43, the...Ch. 3.6 - A fire hose nozzle has a diameter of in. According...Ch. 3.6 - Water flowing from the 0.75-in.-diameter outlet...Ch. 3.6 - Prob. 46PCh. 3.6 - Prob. 47PCh. 3.6 - Prob. 48PCh. 3.6 - The pressure and average velocity at point A in...Ch. 3.6 - Water (assumed inviscid and incompressible) flows...Ch. 3.6 - Prob. 51PCh. 3.6 - Prob. 52PCh. 3.6 - Prob. 53PCh. 3.6 - Prob. 54PCh. 3.6 - Prob. 55PCh. 3.6 - Prob. 56PCh. 3.6 - Water (assumed frictionless and incompressible)...Ch. 3.6 - Prob. 58PCh. 3.6 - Water flows through the pipe contraction shown in...Ch. 3.6 - Prob. 60PCh. 3.6 - Prob. 61PCh. 3.6 - Prob. 62PCh. 3.6 - Prob. 63PCh. 3.6 - Prob. 64PCh. 3.6 - The circular stream of water from a faucet is...Ch. 3.6 - Water is siphoned from the tank shown in Fig....Ch. 3.6 - Prob. 67PCh. 3.6 - Prob. 68PCh. 3.6 - Water is siphoned from the tank shown in Fig....Ch. 3.6 - Prob. 70PCh. 3.6 - Water exits a pipe as a free jet and flows to a...Ch. 3.6 - Water flows steadily from a large, closed tank as...Ch. 3.6 - Prob. 73PCh. 3.6 - Prob. 74PCh. 3.6 - Prob. 75PCh. 3.6 - Prob. 76PCh. 3.6 - Prob. 77PCh. 3.6 - Prob. 78PCh. 3.6 - Prob. 79PCh. 3.6 - Air is drawn into a small open-circuit wing tunnel...Ch. 3.6 - Prob. 81PCh. 3.6 - Water flows steadily from the large open tank...Ch. 3.6 - Prob. 83PCh. 3.6 - Prob. 84PCh. 3.6 - Prob. 85PCh. 3.6 - Prob. 86PCh. 3.6 - Prob. 87PCh. 3.6 - Prob. 88PCh. 3.6 - Prob. 89PCh. 3.6 - Prob. 90PCh. 3.6 - Prob. 91PCh. 3.6 - Prob. 92PCh. 3.6 - Prob. 93PCh. 3.6 - Prob. 94PCh. 3.6 - Prob. 95PCh. 3.6 - Prob. 96PCh. 3.6 - Prob. 97PCh. 3.6 - Prob. 98PCh. 3.6 - Prob. 99PCh. 3.6 - Determine the flowrate through the submerged...Ch. 3.6 - The water clock (clepsydra) shown in Fig. P3.101...Ch. 3.6 - Prob. 102PCh. 3.6 - Prob. 105PCh. 3.6 - Prob. 106PCh. 3.6 - Prob. 107PCh. 3.6 - Prob. 109PCh. 3.6 - Prob. 110PCh. 3.6 - Water flows through the branching pipe shown in...Ch. 3.6 - Prob. 112PCh. 3.6 - Prob. 113PCh. 3.6 - Prob. 114PCh. 3.6 - Prob. 115PCh. 3.6 - Prob. 116PCh. 3.6 - Prob. 117PCh. 3.6 - Prob. 118PCh. 3.6 - Prob. 119PCh. 3.6 - Prob. 120PCh. 3.6 - Prob. 121PCh. 3.6 - Prob. 122PCh. 3.6 - Prob. 123PCh. 3.6 - Water flows in a rectangular channel that is 2.0 m...Ch. 3.6 - Prob. 125PCh. 3.6 - A Venturi meter with a minimum diameter of 3 in....Ch. 3.6 - Prob. 127PCh. 3.6 - Prob. 128PCh. 3.6 - What diameter orifice hole, d, is needed if under...Ch. 3.6 - A weir (see Video V10.13) of trapezoidal cross...Ch. 3.6 - Prob. 131PCh. 3.6 - Water flows under the inclined sluice gate shown...Ch. 3.7 - Water flows in a vertical pipe of 0.15-m diameter...Ch. 3.7 - Prob. 134PCh. 3.7 - Draw the energy line and hydraulic grade line for...Ch. 3.8 - Prob. 137PCh. 3.8 - Prob. 138P
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