System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.22P
The flow rate f in
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A simple model of blood flow through the descending aorta is provided at the right. Total
flow into the aorta is given by Q. The model includes the effects of vessel taper and outflow
through 10 tributary arteries, through which the flow is assumed to be equal and given by
q. We will assume that the blood is in-viscid and that the flow is steady and laminar. The
effects of gravity are neglected.
A₁
P₁
A₂
P₂
Find the pressure (P2) at bottom outlet in terms of Q, P₁, and A₁ for the three cases:
a) For a tapered vessel for which A2 = A₁/2; and q = 0.
b) For a vessel without a taper, but with q = Q/20.
c) For a tapered vessel for which A2 = A₁/2 and q = Q/20.
For a venturi meter given below, the volumetric flow rate is defined in terms of the geometrical parameters, the
density of working fluid (p), and density of the manometer liquid (pm) as
4.
Q = f(D, D2, A2, g, h, Pmv Pr)
%3D
Write down the balance equations and show your work to end up with an expression for the volumetric flow rate in
terms of the variables defined above.
Mechanical EngineeringFluid Mechanics
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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