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
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Ответ:
Explanation:
To find the angular velocity of the tank at which the bottom of the tank is exposed
From the information given:
At rest, the initial volume of the tank is:
where;
height h which is the height for the free surface in a rotating tank is expressed as:
at the bottom surface of the tank;
r = 0, h = 0
∴
0 = 0 + C
C = 0
Thus; the free surface height in a rotating tank is:
Now; the volume of the water when the tank is rotating is:
dV = 2π × r × h × dr
Taking the integral on both sides;
replacing the value of h in equation (2); we have:
Since the volume of the water when it is at rest and when the angular speed rotates at an angular speed is equal.
Then![V_f = V_i](/tpl/images/1084/5930/06bfa.png)
Replacing equation (1) and (3)
Finally, the angular velocity of the tank at which the bottom of the tank is exposed = 10.48 rad/s
Ответ: