Question

Water flows through a capillary tube at the rate of 10 cc per minute. If the pressure difference across the same tube is doubled, the rate of flow of water through the tube will be (in cc per minute):
1) 20
2) 5
3) 40
4) 2.5

Answer 1

Hint: The motion of water through the pipe can be described using the Bernoulli’s theorem and equation of continuity. But there is also one formula which describes it and that is the law of Poiseuille. The law describes the relationship between the flow and the different parameters such as length of the tube, etc.

Complete step by step solution:
According to The Poiseuille law, the flow of liquid such as the water through the pipe depends on the variables such as the length of the tube, radius, pressure gradient and the viscosity of the fluid. The law can be described mathematically as, \[Q=\dfrac{\Delta P\pi {{r}^{4}}}{8\eta l}\],
Where \[\Delta P\]is the pressure gradient, r is the radius of the pipe, \[\eta \] is the viscosity of the liquid flowing through it and l is the length of the pipe.
It is evident from the above relationship that \[Q\propto \Delta P\]. So, If the pressure difference is double, the rate of flow will also get doubled.
\[\Rightarrow Q=20cc/\min \]

So, the correct answer is “Option 1”.

Note:
The pressure gradient is the pressure difference between the two ends of the tube.
Viscosity is the property of the liquid and not of the pipe.
So, for water and for kerosene the values will be different.
The Poiseuille law gives us the resistance offered to the flow of the liquid through the pip