Question

Water is flowing through two horizontal pipes of different radii which are connected together. In the first pipe speed of water is $4{ms}^{-1}$ and the pressure is $1.25\times {10}^4{Nm}^{-2}.$ Then pressure of water in the second pipe is
( radii of those pipes are in the ratio 1:2 )

• A. $0.5\times {10}^4{Nm}^{-2}$
• B. $0.75\times {10}^4{Nm}^{-2}$
• C. $1\times {10}^4{Nm}^{-2}$
• D. $2\times {10}^4{Nm}^{-2}$

Answer 1

The correct option is D $2\times {10}^4{Nm}^{-2}$

$\pi \left(r^2\right)\times 4=\pi \left(4r^2\right)\times V_2$ ( Discharge is same )

$\Rightarrow V_2=1m/s$

Applying Bernoulli's equation

$\Rightarrow \frac{P_1}{Pg}+\frac{r_1^2}{2g}=\frac{P_2}{Pg}+\frac{V_2^2}{2g}$

$\Rightarrow \frac{P_2}{Pg}=\frac{1.25\times {10}^4}{Pg}+\frac{1}{2g}\left(15\right)$

$\Rightarrow P_2=(1.25\times {10}^4+7.5\times {10}^3)N/m^2$

$\Rightarrow P_2=2\times {10}^{4}M/m^2$

Hence, the answer is $P_2=2\times {10}^{4}M/m^2.$