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 10.4, Problem 55P
To determine
The width of the canal.
The bottom slop of the canal.
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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 10 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Ch. 10.2 - Prob. 1PCh. 10.2 - The flowrate per unit width in a wide channel is q...Ch. 10.2 - A rectangular channel 3 m wide carries 10 m3/s at...Ch. 10.2 - Prob. 4PCh. 10.2 - Prob. 5PCh. 10.2 - Prob. 6PCh. 10.2 - Prob. 7PCh. 10.2 - Prob. 8PCh. 10.2 - Prob. 9PCh. 10.2 - Prob. 10P
Ch. 10.2 - Prob. 11PCh. 10.3 - Water flows in a 10-m-wide open channel with a...Ch. 10.3 - Water flows in a 10-ft-wide rectangular channel...Ch. 10.3 - Water flows in a rectangular channel at a rate of...Ch. 10.3 - Water flows in a 5-ft-wide rectangular channel...Ch. 10.3 - Water flows over the bump in the bottom of the...Ch. 10.3 - Water in a rectangular channel flows into a...Ch. 10.3 - A channel has a rectangular cross section, a width...Ch. 10.3 - Prob. 19PCh. 10.3 - Prob. 20PCh. 10.3 - Prob. 23PCh. 10.3 - Prob. 24PCh. 10.3 - Prob. 25PCh. 10.3 - Prob. 26PCh. 10.3 - Prob. 27PCh. 10.3 - Prob. 28PCh. 10.3 - Prob. 29PCh. 10.4 - Water flows in a 5-m-wide channel with a speed...Ch. 10.4 - The following data are taken from measurements on...Ch. 10.4 - Prob. 32PCh. 10.4 - The following data are obtained for a particular...Ch. 10.4 - Prob. 34PCh. 10.4 - Prob. 35PCh. 10.4 - A 2-m-diameter pipe made of finished concrete lies...Ch. 10.4 - By what percent is the flowrate reduced in the...Ch. 10.4 - Prob. 38PCh. 10.4 - Prob. 39PCh. 10.4 - Prob. 40PCh. 10.4 - A trapezoidal channel with a bottom width of 3.0 m...Ch. 10.4 -
Water flows in a 2-m-diameter finished concrete...Ch. 10.4 - A round concrete storm sewer pipe used to carry...Ch. 10.4 - Find the discharge per unit width for a wide...Ch. 10.4 - Water flows down a wide rectangular channel having...Ch. 10.4 - Prob. 46PCh. 10.4 - Prob. 47PCh. 10.4 - Prob. 48PCh. 10.4 - Determine the flowrate for the symmetrical channel...Ch. 10.4 - (See The Wide World of Fluids article titled “Done...Ch. 10.4 - Prob. 51PCh. 10.4 - Prob. 52PCh. 10.4 - Prob. 53PCh. 10.4 - Prob. 54PCh. 10.4 - Prob. 55PCh. 10.4 - Prob. 56PCh. 10.4 - Prob. 57PCh. 10.4 - Prob. 58PCh. 10.4 - Prob. 59PCh. 10.4 - Prob. 60PCh. 10.4 - Prob. 61PCh. 10.4 - Prob. 62PCh. 10.4 - Prob. 63PCh. 10.4 - Water flows 1 m deep in a 2-m-wide finished...Ch. 10.4 - Uniform flow in a sluggish channel having a nearly...Ch. 10.4 - To prevent weeds from growing in a clean...Ch. 10.4 - Prob. 67PCh. 10.4 - Prob. 68PCh. 10.4 - Prob. 69PCh. 10.4 - Prob. 70PCh. 10.5 - Prob. 71PCh. 10.5 - Prob. 72PCh. 10.6 - Water flows upstream of a hydraulic jump with a...Ch. 10.6 - Prob. 75PCh. 10.6 - Prob. 76PCh. 10.6 - Prob. 77PCh. 10.6 - At a given location in a 12-ft-wide rectangular...Ch. 10.6 - Prob. 79PCh. 10.6 - Prob. 80PCh. 10.6 - Prob. 81PCh. 10.6 - A hydraulic engineer wants to analyze steady flow...Ch. 10.6 - Prob. 83PCh. 10.6 - A rectangular sharp-crested weir is used to...Ch. 10.6 - Prob. 85PCh. 10.6 - Prob. 87PCh. 10.6 - Prob. 88PCh. 10.6 - Prob. 89PCh. 10.6 - Prob. 90PCh. 10.6 - Prob. 91PCh. 10.7 - Prob. 1LLPCh. 10.7 - Prob. 2LLPCh. 10.7 - Prob. 3LLP
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