The rate of flow of liquid in a tube of radius r, length l, whose ends are maintained at a pressure difference P is `V = (piQPr^(4))/(etal)` where `eta` is coefficient of the viscosity and Q is

Options

A. `8`
B. `(1)/(8)`
C. `16`
D. `(1)/(16)`

Explanation

To solve the problem, we need to derive the expression for the rate of flow of liquid in a tube and identify the value of Q in the given equation.

### Step-by-Step Solution:

1. **Understanding the Given Formula**:
We are given the formula for the rate of flow of liquid in a tube:
\[ V = \frac{\pi Q P r^4}{\eta l} \]
where:
- \( V \) is the rate of flow,
- \( P \) is the pressure difference,
- \( r \) is the radius of the tube,
- \( \eta \) is the coefficient of viscosity,
- \( l \) is the length of the tube,
- \( Q \) is a constant we need to determine.

2. **Using Poiseuille's Law**:
According to Poiseuille's law, the rate of flow \( V \) through a cylindrical tube is given by:
\[ V = \frac{\pi P r^4}{8 \eta l} \]
This formula describes the flow of a viscous fluid through a pipe.

3. **Comparing the Two Equations**:
To find \( Q \), we can compare the two expressions for \( V \):
\[ \frac{\pi Q P r^4}{\eta l} = \frac{\pi P r^4}{8 \eta l} \]

4. **Canceling Common Terms**:
We can cancel out the common terms \( \pi P r^4 \) from both sides of the equation (assuming \( P \), \( r \), and \( \eta \) are not zero):
\[ Q = \frac{1}{8} \]

5. **Conclusion**:
Thus, the value of \( Q \) is:
\[ Q = \frac{1}{8} \]

### Final Answer:
The value of \( Q \) is \( \frac{1}{8} \).