If the rate of rotational speed of the 3-tube system shown in Fig. P3-135 is
The water height in each tube.
The speed at which the middle limb is completely empty.
Answer to Problem 135P
The height of water in left tube is
The height of water in right tube is
The height of water in middle tube is
The angular speed at which the middle limb is completely empty is
Explanation of Solution
Given information:
The rotational speed of the system is
Write the expression for the water level rises in the left limb.
Here, the distance of the left limb from the axis is
Write the expression for the velocity in the left limb.
Here, the angular speed is
Write the expression for the rise of liquid in the left limb.
Here, the rise in the left limb is
Write the expression for the water level rises in the right limb.
Here, the rise of water in the right limb is
Write the expression for the rise of water in middle limb.
Here, the rise of water in the middle limb is
Write the expression for the angular velocity at which the water height in the middle limb is zero.
Here, the distance between the center and the left limb is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The height of water in left tube is
The height of water in right tube is
The height of water in middle tube is
The angular speed at which the middle limb is completely empty is
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