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  4. Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm-2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm-3)

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Q. Water flows in a horizontal tube (see figure). The pressure of water changes by $700\, Nm^{-2}$ between $A$ and $B$ where the area of cross section are $40\, cm^2$ and $20\, cm^2$, respectively. Find the rate of flow of water through the tube.
(density of water = $1000\, kgm^{-3}$)Physics Question Image

JEE MainJEE Main 2020Mechanical Properties of Fluids

Solution:

Rate of flow of water $= A_AV_A = A_BV_B$
$(40)V_A = (20)V_B$
$V_B=2V_A\,......(1)$
Using Bernoulli's theorem
$P+\frac{1}{2}\rho V^{2}=P_{B}+\frac{1}{2}\rho V^{2}_{B}$
$P_{A}-P_{B}=\frac{1}{2}\rho\left(V^{2}_{B}-V^{2}_{A}\right)$
$700=\frac{1}{2}\times1000\left(4V^{2}_{A}-V^{2}_{A}\right)$
$V_{A}=0.68\,m/s = 68\, cm/s$
Rate of flow $= A_{A}V_{A}$
$-\left(40\right)\left(68\right)=2720\,cm^{3}/s$