The velocity of efflux of a liquid through an orifice in the bottom of a tank does not depend upon

Options

A. density of liquid
B. height of the liquid column above orifice
C. acceleration due to gravity
D. None of the above

Explanation

To solve the problem, we need to analyze the factors that affect the velocity of efflux of a liquid through an orifice at the bottom of a tank. The velocity of efflux can be derived from Torricelli's theorem, which states that the velocity (v) of a fluid flowing out of an orifice under the influence of gravity is given by the equation:

\[ v = \sqrt{2gh} \]

where:
- \( v \) = velocity of efflux,
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, m/s^2 \)),
- \( h \) = height of the liquid column above the orifice.

### Step-by-Step Solution:

1. **Identify the Variables**:
- The velocity of efflux depends on the height of the liquid column (h) and the acceleration due to gravity (g).

2. **Analyze the Equation**:
- From the equation \( v = \sqrt{2gh} \), we can see that the velocity is directly related to the height of the liquid column (h) and the gravitational acceleration (g).

3. **Determine Independence from Density**:
- The equation does not include the density of the liquid (ρ). This indicates that the velocity of efflux is independent of the density of the liquid.

4. **Conclusion**:
- Therefore, the velocity of efflux does not depend on the density of the liquid.

### Final Answer:
The velocity of efflux of a liquid through an orifice in the bottom of a tank does not depend upon the density of the liquid.