Homework 1
Due 09/18/08 at 2:30 pm in 3418C Patrick Taylor (My office)
Problem 1:
Water at 20
◦
C is flowing in a 100mm diameter pipe at an average velocity of 2 m/s. If
the diameter of the pipe is suddenly expanded to 150 mm, what is the new velocity in the
pipe? What is the flowrate in the pipe?
Problem 2:
The velocity profile,
v
(
r
), for turbulent flow in smooth pipes is sometimes estimated by
the seventhroot law, originally proposed by Blasius (1911):
v
(
r
) =
V
o
1

r
R
1
/
7
where
V
o
is the maximum (centerline) velocity and
R
is the radius of the pipe. Calculate
the average velocity and flowrate in the pipe.
Problem 3:
In the pipe system for a given discharge, the ratio of the head loss in a given length of 1
m pipe to the head loss in the same length of 2 m pipe is (a) 2, (b) 4, (c) 16, (d) 32.
Problem 4:
Water leaves a reservoir at 0.06 m
3
/s through a 200 mm riveted steel pipeline that pro
trudes into the reservoir and then immediately turns a 90
◦
bend with a local (minor) loss
coefficient equal to 0.3. Estimate the length of pipeline required for the friction losses to
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 Fall '08
 MOORTHY
 Fluid Dynamics, Velocity, United States customary units

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