Question

Water enters a house through a pipe $2\text{cm}$ inside diameter at an absolute pressure $4\times {10}^5\text{Pa}$ (about $4$ atmospheres). The pipe leading to second floor bathroom $5\text{m}$ above is $1\text{cm}$ in diameter. The flow velocity at the inlet pipe is $4\text{m/s}$. The pressure in the bathroom.

• A. $2\times {10}^5\text{Pa}$
• B. $2.3\times {10}^5\text{Pa}$
• C. $3\times {10}^5\text{Pa}$
• D. $3.3\times {10}^5\text{Pa}$

Answer 1

The correct option is B $2.3\times {10}^5\text{Pa}$

The flow velocity is obtained from the continuity equation

$v_2=\frac{A_1}{A_2}.v_1=\frac{\pi {\left(1.0\right)}^2}{\pi {\left(0.5\right)}^2}\left(4\right)=16\text{m/s}$

The pressure is obtained from Bernoulli's equation

$p_2=p_1-\frac{1}{2}\rho (v_2^2-v_1^2)-\rho g(y_2-y_1)$

$p_2=4\times {10}^5-\frac{1}{2}\times 1\times {10}^3(256-16)-1\times {10}^3\times 9.8\times 5=2.3\times {10}^5\text{Pa}$

$\therefore \left(b\right)$