A cylindrical vessel of area of cross section `A` is filled with a liquid up to a height `H`. A very small hole of area of cross section a is made at the bottom of the vellel. Find the time taken by the vessel to become empty.
Text Solution
AI Generated Solution
To find the time taken by a cylindrical vessel to become empty when a small hole is made at the bottom, we can follow these steps:
### Step 1: Understand the Problem
We have a cylindrical vessel with a cross-sectional area \( A \) filled with liquid to a height \( H \). A small hole with a cross-sectional area \( a \) is made at the bottom. We need to find the time \( t \) it takes for the vessel to empty completely.
### Step 2: Apply the Continuity Equation
According to the continuity equation, the flow rate of the liquid must be constant. Therefore, we can write:
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