1. Tardigrade
  2. Question
  3. Physics
  4. Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is V. If the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is $V$. If the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become

COMEDKCOMEDK 2015Mechanical Properties of Fluids

Solution:

According to Poiseuille's formula, rate of flow through a narrow tube $V = \frac{\pi Pr^4}{8 \eta l}$
For given $P$ and $\eta , V \propto \frac{r^4}{l} \therefore \:\: \frac{V_1}{V_2} = \frac{r^4_1}{r_2^4} \times \frac{l_2}{l_1}$
, Here, $V_1 = V, r_2 = r_1 /2 , l_2 = 2l_1, V_2 = ?$
So, $\frac{V}{V_2} = (2)^4 \times 2 = 32 , V_2 = \frac{V}{32}$