Question

The rate of flow of liquid through an orifice at the bottom of a tank does not depend on

• A. The size of orifice
• B. Density of liquid
• C. The height of fluid column
• D. Acceleration due to gravity

Answer 1

The correct option is B

Density of liquid

Explanation for the correct option

Option B:

An orifice is any opening, mouth, hole or vent, as in a pipe, a plate, or a body.

1. Let the area of orifice =$A$
2. Height upto which it is filled =$h$
3. The velocity flux is given by the formula = $v=\sqrt{2gh}wheregisaccelerationduetogravity$
4. Rate of discharge is given by $\frac{dv}{dt}=Av=A\sqrt{2gh}$
5. So, we can see that density does not effect the rate of flow.

Explanation for the correct option

Option A:

1. Let the area of orifice =$A$
2. Height upto which it is filled =$h$
3. The velocity flux is given by the formula = $v=\sqrt{2gh}wheregisaccelerationduetogravity$
4. Rate of discharge is given by $\frac{dv}{dt}=Av=A\sqrt{2gh}$
5. We can see that it depends upon the size of orifice.

Option C:

1. Let the area of orifice =$A$
2. Height upto which it is filled =$h$
3. The velocity flux is given by the formula = $v=\sqrt{2gh}wheregisaccelerationduetogravity$
4. Rate of discharge is given by $\frac{dv}{dt}=Av=A\sqrt{2gh}$
5. We can see that it depends upon height of column.

Option D:

1. Let the area of orifice =$A$
2. Height upto which it is filled =$h$
3. The velocity flux is given by the formula = $v=\sqrt{2gh}wheregisaccelerationduetogravity$
4. Rate of discharge is given by $\frac{dv}{dt}=Av=A\sqrt{2gh}$
5. We can see that it depends upon acceleration due to gravity.

Hence, option B is correct.