Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 41P
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The work input required to inflate the bubble.
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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
Fundamentals Of Thermal-fluid Sciences In Si Units
Ch. 10 - Prob. 1PCh. 10 - Define incompressible flow and incompressible...Ch. 10 - Define internal, external, and open-channel...Ch. 10 - What is the no-slip condition? What causes it?
Ch. 10 - What is forced flow? How does it differ from...Ch. 10 - What is a boundary layer? What causes a boundary...Ch. 10 - What is cavitation? What causes it?
Ch. 10 - Does water boil at higher temperatures at higher...Ch. 10 - If the pressure of a substance is increased during...Ch. 10 - What is vapor pressure? How is it related to...
Ch. 10 - The analysis of a propeller that operates in water...Ch. 10 - A pump is used to transport water to a higher...Ch. 10 - In a piping system, the water temperature remains...Ch. 10 - The analysis of a propeller that operates in water...Ch. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - How does the dynamic viscosity of (a) liquids and...Ch. 10 - Consider two identical small glass balls dropped...Ch. 10 - The viscosity of a fluid is to be measured by a...Ch. 10 - Prob. 21PCh. 10 - Consider the flow of a fluid with viscosity μ...Ch. 10 - A thin 30-cm × 30-cm flat plate is pulled at 3 m/s...Ch. 10 - A rotating viscometer consists of two concentric...Ch. 10 - Prob. 25PCh. 10 - The dynamic viscosities of carbon dioxide at 50°C...Ch. 10 - Prob. 28PCh. 10 - For flow over a plate, the variation of velocity...Ch. 10 - In regions far from the entrance, fluid flow...Ch. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - A large plate is pulled at a constant speed of U =...Ch. 10 - Prob. 35PCh. 10 - A small-diameter tube is inserted into a liquid...Ch. 10 - Prob. 37PCh. 10 - Prob. 38PCh. 10 - Is the capillary rise greater in small-or...Ch. 10 - Prob. 40PCh. 10 - Prob. 41PCh. 10 - A 1.2-mm-diameter tube is inserted into an unknown...Ch. 10 - Determine the gage pressure inside a soap bubble...Ch. 10 - A 0.03-in-diameter glass tube is inserted into...Ch. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - A capillary tube is immersed vertically in a water...Ch. 10 - Prob. 48PCh. 10 - Prob. 49PCh. 10 - Prob. 50RQCh. 10 - Consider a 55-cm-long journal bearing that is...Ch. 10 - Prob. 52RQCh. 10 - The pressure on the suction side of pumps is...Ch. 10 - Consider laminar flow of a Newtonian fluid of...Ch. 10 - Prob. 56RQCh. 10 - Prob. 57RQCh. 10 - Some rocks or bricks contain small air pockets in...
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