Review Innovations CE Review for Nov 2023 - Hydraulics 7
ROTATING VESSEL
4. A closed cylinder 1.0 m Ø and 2.0 m high contains water
1.5 m deep, the remaining air space being under a
pressure of 120 kPa.
a. Compute the pressure at the center of the bottom if
ω = 12 rad/s.
b. Compute the pressure at the circumference of the
bottom.
c. What ω will just zero the depth of water at the center.
d. How much area of the bottom is not covered with
water if ω = 20 rad/s?
5. An open 1 – m diameter tank contains water at a depth of
0.7 m when at rest. As the tank is rotated about its vertical
axis, the center of the fluid surface is depressed. At what
angular velocity will the bottom of the tank first be
exposed? No water is spilled from the tank.
Ans. 10.5 rad/sec
6. An open, 0.60-m-diameter tank contains water to a depth
of 1.0 m when at rest. If the tank is rotated about its
vertical axis with an angular velocity of 180 rev/min,
what is the minimum height of the tank walls to prevent
2 x water from spilling over the sides?
tan Ans. 1.815 m
g
7. A closed, 0.4-m-diameter cylindrical tank is completely
Where tan θ is the slope at the surface of paraboloid at any filled with oil (SG = 0.9) and rotates about its vertical
distance x from the axis of rotation. longitudinal axis with an angular velocity of 40 rad/s.
Determine the difference in pressure just under the vessel
2 x 2 cover between a point on the circumference and a point
y on the axis.
2g
Ans. 28.8 kPa
By squared-property of parabola, 8. The three-legged manometer shown is filled with water to
a depth of 20 cm. All tubes are long and have equal small
r2 x 2 diameters. If the system spins at angular velocity of 120
h y rpm about the central tube,
a. Find the height in cm in the central tube. [Hint: The
central tube must supply water to both the outer
Important conversion factor
legs.]
Ans. 14.7
1 b. Find the height in cm in the outer tube.
1 rpm = rad/sec
30 Ans. 22.7
1. Determine the rpm required for an open 100-cm Ø
cylindrical tank 250 cm high, containing water 150 cm
deep, so that:
a. Water could just reach the rim of the tank.
b. The depth of water at center is zero.
c. There is no water at the bottom within 20 cm from
the axis of rotation.
2. An open cylindrical tank 800 mm in diameter and 2000 mm
high contains water to a depth of 1.6 m. It is rotated about
its vertical axis at 13 rad/s. How many liters of water are
spilled?
9. An open cylindrical tank, 1.0 m in diameter and 2.0 m high
3. A 1-m Ø closed cylindrical vessel with vertical axis is 3 m
has 1.5 m water,
high. It is filled with water with a pressure of 290 kPa at
a. What constant rpm can be given to the cylinder
the top. The wall is 4 mm thick. If the vessel is rotated at
without causing any water to spill? Ans. 84.6
360 rpm, b. What is the pressure at the center of the bottom of
a. Determine the total pressure against the top. the tank when it is rotated at 57.3 rpm? Ans. 12.5 kPa
b. Determine the maximum intensity of hoop tension. c. What is the pressure at the circumference of the
c. Determine the force of water against the wall.
bottom of the tank when it is rotated at 57.3 rpm?
Ans. 17 kPa
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