Question

Water flows through a horizontal tube of variable cross section figure. The area of cross section at A and B are 4 $m{m}^2$ and 2$m{m}^2$ respectively. If 1 cc of water enters per second through A, find (a) the speed of water at A, (b) the speed of water at B and (c) the pressure difference $P_A—P_B$.

Answer 1

(a) Given,

$\frac{Q_A}{t}=\frac{1a}{sec}$ = discharge

$\Rightarrow a_A\times V_A=Q_A$

$\Rightarrow 4\times {10}^{-2}\times V_A=1$ cc/sec

[because, $a_{A}4m^2=4\times {10}^{-2}c{m}^2$]

$\Rightarrow V_A$ = 25 m/sec

(b) $a_A\times V_A=a_B\times V_B$

$\Rightarrow 4\times {10}^{-2}\times 25=2\times {10}^{-2}\times V_B$

$\Rightarrow V_B$ = 50 cm/sec

(c) From Bernoulli's equation,

$\frac{1}{2}\rho v_A^2+\rho v_B^2+{\rho }_B$

$\Rightarrow (P_A-P_B)=\frac{1}{2}\rho (v_B^2-v_A^2)$

= $\frac{1}{2}\times 1\times (2500-625)$

=$\frac{1875}{2}$

= $937.5\frac{\text{Dyne}}{c{m}^2}$

= 93.75 $N/m^2$

= 94 $N/m^2$