A `U`-tube rotates with angular velocity `omega` about the vertical axis `AB`. What is the difference in fluid level h in terms of `omega` the radii `r_(1)` and `r_(2)` and the fluid density `rho?`
Text Solution
AI Generated Solution
To solve the problem of finding the difference in fluid level \( h \) in a rotating U-tube in terms of angular velocity \( \omega \), the radii \( r_1 \) and \( r_2 \), and the fluid density \( \rho \), we can follow these steps:
### Step 1: Understand the System
The U-tube is rotating about a vertical axis, which means that the fluid inside the U-tube experiences a centripetal acceleration due to the rotation. The pressure in a fluid at rest increases with depth, but in this case, we need to consider the effect of rotation.
### Step 2: Determine the Centripetal Acceleration
The centripetal acceleration \( a_c \) at a distance \( r \) from the axis of rotation is given by:
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