Question

Water flows with a velocity $V$ in a tube of diameter d and the rate of flow is $Q$ . Another tube of diameter $2d$ is coupled to the first one. The velocity of water flowing out and rate of flow in the second tube are respectively:

• A. $\frac{V}{4}$ and $Q$
• B. $\frac{V}{4}$ and $\frac{Q}{2}$
• C. $2V$ and $2Q$
• D. $\frac{V}{2}$ and $2Q$

Answer 1

The correct option is A $\frac{V}{4}$ and $Q$

In 1st case, from poiseullis eqn,
$Q=\frac{\pi r^{4}p}{8\eta L}$
So,
As,2nd pipe is coupled to first the rate of flow will remain same as Q
So,
$V=\frac{Q}{\pi r^2}$
V 2nd tube$=\frac{Q}{\pi {\left(2r\right)}^2}=\frac{V}{4}$
So,
Velocity of water flowing out$=\frac{V}{4}$
Rate of flowing in 2nd tube $=Q$