Download HYDRODYNAMICS

Isfahan University of Technology (IUT) Department of Civil Engineering
FLUID MECHANICS
1385-1386
Term II
Assignment #4
Motion of fluid particles, part II
Due: 27/1/1386
__________________________________________________________________
1
2
3*
A Pelton wheel turbine is illustrated in the figure.
The radius to the line of action of the tangential
reaction on each vane is 1 ft. Each vane deflects
fluid by an angle of 135 as indicated. Assume that
all of the flow occurs in a horizontal plane. Each of
the four jets shown strikes a vane with a velocity of
100 ft/s and a stream diameter of 1 in. The
magnitude of velocity of the jet remains constant
along the vane surface. How much torque is
required to hold the wheel stationary?
A 2-ft-diameter cylindrical drum of water,
lying on its side, is being emptied through a
2-in-diameter hole at the bottom of the
drum. The velocity of the water out of the
hole is 2gh , where h is the height of the
water surface above the outlet of the tank.
Initially the tank is half-full. Find the time
for the tank to empty.
135
1 ft
1 in.
Vent
2 ft
2 in.
h
4 ft
V
A pump transfers water from one reservoir to another as shown in the figure. The friction
head loss in the pipe is given by KLV2/2g, where V is the average fluid velocity in the pipe
and KL is the loss coefficient. The relation between the pump head (hP) and the flowrate
through the pump is given in the figure. If KL = 20, and the pipe diameter is 4 in., what is
the flowrate through the pump?
hP (m)
300
200
100 ft
100
Pump
0
0
4
1
Q (ft 3/s)
2
3
If the flow of Prob. #2 is assumed to be quasi-steady, find a relationship between the water
depth, h, and time, t.
1
Assignment #4
Motion of fluid particles, part II
Due: 25/1/1386
__________________________________________________________________
5
For the system
shown in the figure,
find the maximum
power that can be
extracted from the
turbine in terms of
, D, and h (neglect
all losses).
h
D
T
6*
An inviscid liquid drains from a large tank
through a square duct of width b as shown in
the figure. The velocity of the fluid at the outlet
is not precisely uniform because of the
h
difference in elevation across the outlet. If
b<<h, this difference in velocity is negligible.
x
For given b and h, determine v as a function of
v= v(x)
b
b/2
x and integrate the results to determine the
average velocity, V.
Plot the velocity
distribution, v = v(x), across the outlet if h = 1
m and b = 0.1, 0.2, 0.4, 0.6, 0.8, and 1 m. How
small must b be if the difference between the centerline velocity, v at x = b/2, and the
average velocity is less than within 3% of the average velocity?
7*
Salt water flows from tank A through a hole with diameter d = 100
mm, as indicated in the figure. Initially (time = 0) tank A contains
concentrated salt water with a specific gravity of 1.15 and tank B
contains pure water. Each tank has a diameter of 2 m and initial liquid
depth of 3 m. Prove that the specific gravity of the liquid in tank B as
a function of time can be expressed as,
SG 
6.45  1.15 1.732  0.221t 
6  1.732  0.221t 
2
A
2m
d
2
Neglect viscous effects and assume that the liquid in tank B is mixed
continuously so that the specific gravity is uniform throughout the
tank. Also assume that the flow is quasi-steady (Bernoulli equation
can be used). How long does it take for tank A to be emptied?
2
B
2m