Question

Water is flowing with a velocity of 2 m/s in a horizontal pipe with cross-sectional area decreasing from $2\times {10}^{-2}{m}^2$ to $0.01m^2$ at pressure $4\times {10}^4$ Pascal. The pressure at smaller cross-section in Pascal will be:

• A. $3.2\times {10}^2$
• B. $3.4\times {10}^3$
• C. $3.4\times {10}^4$
• D. $3.4\times {10}^5$

Answer 1

The correct option is C $3.4\times {10}^4$

Using equation of continuity, we can find the velocity at another point. we have
$a_1{v}_1=a_2{v}_2\Rightarrow (2\times {10}^{-2})\times 2=0.01\times v_2\Rightarrow v_2=4m/s$

According to Bernoulli's theorem, for water at same height
$\Delta P=\frac{\rho (v_1^2-v_2^2)}{2}\Rightarrow \Delta P=\frac{1000\times (2^2-4^2)}{2}=-6000Pa\Rightarrow P_2-P_1=-6000Pa\Rightarrow P_2-40000=-6000Pa\Rightarrow P_1=34000Pa=3.4\times {10}^{4}Pa$