The rate of flow of liquid through a capillary tube in an experiment to determine the viscosity of the liquid increases

Options

A. when the pressure of the tube is increased
B. when the length of the tube is increased
C. when the radius of the tube is decreased
D. none of the above

Answer

To solve the question regarding the rate of flow of liquid through a capillary tube and how it relates to viscosity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The rate of flow of liquid (Q) through a capillary tube can be described by Poiseuille's Law, which states:
\[ Q = \frac{\pi \Delta P r^4}{8 \eta L} \]
where \( \Delta P \) is the pressure difference, \( r \) is the radius of the tube, \( \eta \) is the viscosity of the liquid, and \( L \) is the length of the tube.

2. **Effect of Pressure (\( \Delta P \))**: According to the equation, the flow rate \( Q \) is directly proportional to the pressure difference \( \Delta P \). Therefore, if the pressure increases, the flow rate \( Q \) also increases. This means that when the pressure increases, the viscosity of the liquid does not directly increase; instead, the flow rate increases.

3. **Effect of Length (\( L \))**: The equation shows that \( Q \) is inversely proportional to the length of the tube \( L \). Thus, if the length of the tube increases, the flow rate \( Q \) will decrease. Therefore, increasing the length of the tube is not favorable for increasing the flow rate.

4. **Effect of Radius (\( r \))**: The flow rate \( Q \) is directly proportional to the fourth power of the radius of the tube. If the radius decreases, the flow rate \( Q \) will also decrease. Hence, a decrease in the radius is not favorable for increasing the flow rate.

5. **Conclusion**: Based on the above analysis:
- Increasing pressure increases flow rate (correct).
- Increasing length decreases flow rate (incorrect).
- Decreasing radius decreases flow rate (incorrect).

Therefore, the correct option is that the rate of flow of liquid through a capillary tube increases when the pressure increases.

### Final Answer:
The correct option is **A**: The rate of flow of liquid through a capillary tube increases when the pressure increases.

---