The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the tube by Poiseuille law AP = R4Q where the term R, is known as hydraulic resistance, given by 8ul with L = length of the tube, r = inner radius and u = dynamic viscosity coefficient. The value of the coefficient depends on the specific fluid and, in general varies with temperature. For
The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the tube by Poiseuille law AP = R4Q where the term R, is known as hydraulic resistance, given by 8ul with L = length of the tube, r = inner radius and u = dynamic viscosity coefficient. The value of the coefficient depends on the specific fluid and, in general varies with temperature. For
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Problem 2
The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the
tube by Poiseuille law
AP = R4Q
where the term R, is known as hydraulic resistance, given by
8µl
with L = length of the tube, r = inner radius and u = dynamic viscosity coefficient. The value
of the coefficient u depends on the specific fluid and, in general varies with temperature. For
water, it can range between ca. 1.3 [mPa-s] at 10 °C and ca. 0.3 (mPa-s] at 90 °c.
Suppose then the temperature of the water flow in a tube to be a r.v. uniformly distributed
between 90 and 10 °C, so that also u is a r.v. uniformly distributed between 0.3 and 1.3
[mPa•s]
a) Find the mean and variance of u.
8L
b) Letting = 2.5 · 10*, so that Ry = 2.5 · 10*µ, find the pdf of Ry.
c) The fluidity f is defined as the inverse of viscosity (F = 1/u). Find the pdf of F.
d) Compute the mean and variance of f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd54fbc2-091c-4efc-a0ae-33f00779b90d%2Faa2a5bdc-77f5-4dd6-9ec7-2c7031720a2c%2Ftt1i2ju_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2
The volume flowrate Q of a fluid in a tube is related to the pressure difference AP across the
tube by Poiseuille law
AP = R4Q
where the term R, is known as hydraulic resistance, given by
8µl
with L = length of the tube, r = inner radius and u = dynamic viscosity coefficient. The value
of the coefficient u depends on the specific fluid and, in general varies with temperature. For
water, it can range between ca. 1.3 [mPa-s] at 10 °C and ca. 0.3 (mPa-s] at 90 °c.
Suppose then the temperature of the water flow in a tube to be a r.v. uniformly distributed
between 90 and 10 °C, so that also u is a r.v. uniformly distributed between 0.3 and 1.3
[mPa•s]
a) Find the mean and variance of u.
8L
b) Letting = 2.5 · 10*, so that Ry = 2.5 · 10*µ, find the pdf of Ry.
c) The fluidity f is defined as the inverse of viscosity (F = 1/u). Find the pdf of F.
d) Compute the mean and variance of f.
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