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BITSAT 2022
Exam
BITSAT
Year
2022
Subject
Physics
Chapter
Mechanical Properties of Fluids

BITSAT 2022 · Physics · Mechanical Properties of Fluids

A capillary tube is attached horizontally to a constant heat...

A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 25%25 \%, then the rate of flow of liquid will change nearly by

Options

  1. A100%100 \%
  2. B112%112 \%
  3. C124%124 \%
  4. D144%144 \%

Correct answer

D. 144%144 \%

Step-by-step solution

Liquid volume coming out of the tube per second V=pπr48ηl⇒⇒V2V1=[r2r1]4⇒V2=V1[125100]4=V1(54)4⇒ So, now ΔVV=V2−V1V1=(244)V1−V1V1=144%\begin{aligned}& \quad V=\frac{p \pi r^4}{8 \eta l}\\ & \Rightarrow \\ & \Rightarrow \frac{V_2}{V_1}=\left[\frac{r_2}{r_1}\right]^4 \Rightarrow V_2=V_1\left[\frac{125}{100}\right]^4=V_1\left(\frac{5}{4}\right)^4 \\ & \Rightarrow \\ & \text{ So, now } \frac{\Delta V}{V}=\frac{V_2-V_1}{V_1}=\frac{(244) V_1-V_1}{V_1}=144 \% \end{aligned}
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