Question

An incompressible non-viscous fluid (density $\delta$) flows steadily through a cylindrical pipe which has radius $2$R at point A and radius R at point B(at the same height as A) further along the flow direction. If the velocity and pressure at point A are v and P, respectively, find the pressure at B.

Answer 1

By equation of continuity

$A_1{v}_1=A_2{v}_2$

$\pi 4R^{2}v=\pi R^2{v}_2$

$v_2=4v$

by bernoulli's equation $△P=\frac{1}{2}\varrho (v_2^2-v_1^2)$

$P_B-P_A=\frac{15}{2}\varrho v^2$

$P_B=P+\frac{15}{2}\varrho v^2$