Two water pipes P and Q having diameters 2 ti | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: Diameter of pipe $P$,$d_{p} = 2 	imes 10^{-2} \ m$,so radius $r_{p} = 10^{-2} \ m$.Diameter of pipe $Q$,$d_{q} = 4 	imes 10^{-2} \ m$,so

Vedclass · Accepted Answer

$4$ times that of $Q$

Vedclass · Answer

(A) Given: Diameter of pipe $P$,$d_{p} = 2 	imes 10^{-2} \ m$,so radius $r_{p} = 10^{-2} \ m$.Diameter of pipe $Q$,$d_{q} = 4 	imes 10^{-2} \ m$,so radius $r_{q} = 2 	imes 10^{-2} \ m$.According to the equation of continuity,the product of cross-sectional area and velocity is constant for an incompressible fluid: $A_{p}v_{p} = A_{q}v_{q}$.Therefore,the velocity is inversely proportional to the cross-sectional area: $\frac{v_{p}}{v_{q}} = \frac{A_{q}}{A_{p}}$.Since $A = \pi r^{2}$,we have $\frac{v_{p}}{v_{q}} = \frac{\pi r_{q}^{2}}{\pi r_{p}^{2}} = \left(\frac{r_{q}}{r_{p}}ight)^{2}$.Substituting the values: $\frac{v_{p}}{v_{q}} = \left(\frac{2 	imes 10^{-2}}{10^{-2}}ight)^{2} = (2)^{2} = 4$.Thus,$v_{p} = 4v_{q}$. The velocity of water in pipe $P$ is $4$ times that of $Q$.

Two water pipes $P$ and $Q$ having diameters $2 \times 10^{-2} \ m$ and $4 \times 10^{-2} \ m$,respectively,are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is

Similar Questions

What is steady flow?

Two water pipes $P$ and $Q$ having diameters $2 \times 10^{-2} \, m$ and $4 \times 10^{-2} \, m$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is ........

Explain critical speed,white water rapids,and turbulent flow.

In a streamlined flow,the velocity of a fluid at a given point

$A$ horizontal tube of non-uniform cross-section has radii of $0.1\,m$ and $0.05\,m$ respectively at $M$ and $N$. For a streamline flow of liquid, the rate of liquid flow is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module