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 5.3, Problem 109P
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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 5 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Ch. 5.1 - Prob. 1PCh. 5.1 - An incompressible fluid flows horizontally in the...Ch. 5.1 - Water flows steadily through the horizontal piping...Ch. 5.1 - Water flows out through a set of thin, closely...Ch. 5.1 - Estimate the rate (in gal/hr) that your car uses...Ch. 5.1 - The pump shown in Fig. P5.6 produces a steady flow...Ch. 5.1 - The fluid axial velocities shown in Fig. P5.7 are...Ch. 5.1 - The human circulatory system consists of a complex...Ch. 5.1 - Air flows steadily between two cross sections in a...Ch. 5.1 - A hydraulic jump (see Video V10.11) is in place...
Ch. 5.1 - A woman is emptying her aquarium at a steady rate...Ch. 5.1 - An evaporative cooling tower (see Fig. P5.12) is...Ch. 5.1 - At cruise conditions, air flows into a jet engine...Ch. 5.1 - Water at 0.1 m3/s and alcohol (SG = 0.8) at 0.3...Ch. 5.1 - In the vortex tube shown in Fig. P5.15, air enters...Ch. 5.1 - Molten plastic at a temperature of 510 °F is...Ch. 5.1 - A water jet pump (see Fig. P5.17) involves a jet...Ch. 5.1 - To measure the mass flowrate of air through a...Ch. 5.1 - Two rivers merge to form a larger river as shown...Ch. 5.1 - Various types of attachments can be used with the...Ch. 5.1 - An appropriate turbulent pipe flow velocity...Ch. 5.1 - As shown in Fig. P5.22, at the entrance to a...Ch. 5.1 - Prob. 23PCh. 5.1 - Oil for lubricating the thrust bearing shown in...Ch. 5.1 - Flow of a viscous fluid over a flat plate surface...Ch. 5.1 - Air at standard conditions enters the compressor...Ch. 5.1 - Estimate the time required to fill with water a...Ch. 5.1 - For an automobile moving along a highway, describe...Ch. 5.1 - A water jet leaves a fixed nozzle with a velocity...Ch. 5.1 - A hypodermic syringe (see Fig. P5.30) is used to...Ch. 5.1 - Figure P5.31 shows a two-reservoir water supply...Ch. 5.1 - The Hoover Dam (see Video V2.4) backs up...Ch. 5.1 - Storm sewer backup causes your basement to flood...Ch. 5.1 - (See The Wide World of Fluids article “‘Green’...Ch. 5.2 - Prob. 35PCh. 5.2 - When a baseball player catches a ball, the force...Ch. 5.2 - Find the horizontal and vertical forces to hold...Ch. 5.2 - Water flows through a horizontal bend and...Ch. 5.2 - Find the magnitude of the force F required to hold...Ch. 5.2 - Water enters the horizontal, circular...Ch. 5.2 - A truck carrying chickens is too heavy for a...Ch. 5.2 - Exhaust (assumed to have the properties of...Ch. 5.2 - Air at T1 = 300 K, p1 = 303 kPa, and V1 = 0.5 m/s...Ch. 5.2 - Water flows steadily from a tank mounted on a cart...Ch. 5.2 - Determine the magnitude and direction of the...Ch. 5.2 - Figure P5.46 shows a lateral pipe fitting. This...Ch. 5.2 - Water flows steadily between fixed vanes, as shown...Ch. 5.2 - The hydraulic dredge shown in Fig. P5.48 is used...Ch. 5.2 - A static thrust stand is to be designed for...Ch. 5.2 - A vertical jet of water leaves a nozzle at a speed...Ch. 5.2 - A horizontal, circular cross-sectional jet of air...Ch. 5.2 - Calculate the pressure change (p2 − p1) for the...Ch. 5.2 - Air flows into the atmosphere from a nozzle and...Ch. 5.2 - Water flows from a large tank into a dish as shown...Ch. 5.2 - Figure P5.55 shows the configuration of the center...Ch. 5.2 - The plate shown in Fig. P5.56 is 0.5 m wide...Ch. 5.2 - Two water jets of equal size and speed strike each...Ch. 5.2 - Figure P5.58 shows coal being dropped from a...Ch. 5.2 - Determine the magnitude of the horizontal...Ch. 5.2 - Water flows steadily into and out of a tank that...Ch. 5.2 - The rocket shown in Fig. P5.61 is held stationary...Ch. 5.2 -
Air discharges from a 2-in.-diameter nozzle and...Ch. 5.2 - Water is sprayed radially outward over 180° as...Ch. 5.2 - A sheet of water of uniform thickness (h = 0.01 m)...Ch. 5.2 - The results of a wind tunnel test to determine the...Ch. 5.2 - A variable mesh screen produces a linear and...Ch. 5.2 - Prob. 67PCh. 5.2 - Prob. 68PCh. 5.2 - Prob. 69PCh. 5.2 - A Pelton wheel vane directs a horizontal, circular...Ch. 5.2 - Prob. 71PCh. 5.2 - Thrust vector control is a technique that can be...Ch. 5.2 - Prob. 73PCh. 5.2 - Prob. 74PCh. 5.2 - Prob. 75PCh. 5.2 - Prob. 76PCh. 5.2 - (See The Wide World of Fluids article titled “Bow...Ch. 5.2 - Water flows from a two-dimensional open channel...Ch. 5.2 - Prob. 79PCh. 5.2 - A snowplow mounted on a truck clears a path 12 ft...Ch. 5.2 - Prob. 81PCh. 5.2 - Water at 60 °F is flowing through the 2-in. steel...Ch. 5.2 - Five liters/s of water enter the rotor shown in...Ch. 5.2 - Figure P5.84 shows a simplified sketch of a...Ch. 5.2 - The hydraulic turbine shown in Fig. P5.85 has a 10...Ch. 5.2 - Prob. 86PCh. 5.2 -
Calculate the torque required to drive the pump...Ch. 5.2 - Prob. 88PCh. 5.2 - Prob. 89PCh. 5.2 - Prob. 90PCh. 5.3 - Distinguish between shaft work and other kinds of...Ch. 5.3 - Prob. 92PCh. 5.3 - A horizontal Venturi flow meter consists of a...Ch. 5.3 - Figure P5.94 shows the mixing of two streams. The...Ch. 5.3 - Liquid water at 40 °F flows down a vertical,...Ch. 5.3 - A simplified schematic drawing of the carburetor...Ch. 5.3 - Oil (SG = 0.9) flows downward through a vertical...Ch. 5.3 - An incompressible liquid flows steadily along the...Ch. 5.3 - Prob. 99PCh. 5.3 - A water siphon having a constant inside diameter...Ch. 5.3 - Figure P5.101 shows a test rig for evaluating the...Ch. 5.3 - For the 180° elbow and nozzle flow shown in Fig....Ch. 5.3 - An automobile engine will work best when the back...Ch. 5.3 - (See The Wide World of Fluids article titled...Ch. 5.3 - Based on flowrate and pressure rise information,...Ch. 5.3 - Oil (SG = 0.88) flows in an inclined pipe at a...Ch. 5.3 - The pumper truck shown in Fig. P5.107 is to...Ch. 5.3 - The hydroelectric turbine shown in Fig. P5.108...Ch. 5.3 - A pump is to move water from a lake into a large,...Ch. 5.3 - Water is pumped from the tank shown in Fig....Ch. 5.3 - Water is pumped steadily through the apparatus...Ch. 5.3 - Water is pumped from the large tank shown in Fig....Ch. 5.3 - Water flows by gravity from one lake to another as...Ch. 5.3 - The turbine shown in Fig. P5.114 develops 100 hp...Ch. 5.3 - Prob. 115PCh. 5.3 - Water is to be moved from one large reservoir to...Ch. 5.3 - Determine the volume flow rate and minimum power...Ch. 5.3 - Prob. 118PCh. 5.3 - Water is to be pumped from the large tank shown in...Ch. 5.3 - Prob. 120PCh. 5.3 - When the pump shown in Fig. P5.121 is stopped,...Ch. 5.3 - Air flows past an object in a pipe of 2-m diameter...Ch. 5.3 - Water flows steadily down the inclined pipe as...Ch. 5.3 - When fluid flows through an abrupt expansion as...Ch. 5.3 - Water (60 °F) flows through an annular space...Ch. 5.3 - Find the acceleration of the cart shown in Fig....Ch. 5.3 - Prob. 128PCh. 5.3 - Water flows vertically upward in a circular cross-...Ch. 5.3 - Prob. 130PCh. 5.3 - The cross-sectional area of a rectangular duct is...Ch. 5.3 - A small fan moves air at a mass flowrate of 0.004...Ch. 5.3 - Air enters a radial blower with zero angular...Ch. 5.3 - Water enters a pump impeller radially. It leaves...Ch. 5.3 - Water enters an axial-flow turbine rotor with an...Ch. 5.3 - An inward flow radial turbine (see Fig. P5.136)...Ch. 5.5 - Prob. 1LLPCh. 5.5 - Prob. 2LLPCh. 5.5 - Prob. 3LLPCh. 5.5 - Prob. 4LLP
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