When a liquid moves steadily under some pressure through a horizontal tube, it moves in the form of cylindrical layers coaxial to the ends of the tube. The velocity of different layers is different. The velocity of the layer is maximum along the axis of the tube and it decreases as one moves towards the walls of the tube. According to Poiseuille, the rate of flow of liquid through a horizontal capillary tube varies as the relation `V alpha (pr^(4))/(eta l)` where `l` and `r` are the length and radius of the tube and `p` is the pressure different between the ends of the tube and is the constant of proportionality.
The dimensional formula for rate of flow

Options

A. `MLT^(-2)`
B. `M^(0)L^(3)T^(-1)`
C. `MLT^(-1)`
D. `ML^(2)T^(-3)`

Answer

To find the dimensional formula for the rate of flow (volume flow rate) of a liquid through a horizontal capillary tube, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Volume Flow Rate (V)**:
- The volume flow rate (V) is defined as the volume of fluid that passes through a given surface per unit time. Its unit is cubic meters per second (m³/s).

2. **Identify the Units**:
- The unit of volume is cubic meters (m³).
- The unit of time is seconds (s).

3. **Express the Volume Flow Rate in Terms of Dimensions**:
- The dimensional formula for volume (V) is given by:
\[ \text{Volume} = \text{Length}^3 = L^3 \]
- The dimensional formula for time (T) is:
\[ \text{Time} = T \]

4. **Combine the Dimensions**:
- Since the volume flow rate is volume per unit time, we can express it as:
\[ V = \frac{\text{Volume}}{\text{Time}} = \frac{L^3}{T} \]

5. **Write the Dimensional Formula**:
- Therefore, the dimensional formula for volume flow rate (V) is:
\[ [V] = L^3 T^{-1} \]
- In standard format, we can express this as:
\[ M^0 L^3 T^{-1} \]

### Final Answer:
The dimensional formula for the rate of flow (volume flow rate) is:
\[ M^0 L^3 T^{-1} \]