Water flows in a horizontal tube (see figure). The pressure of water changes by $700 \mathrm{Nm}^{-2}$ between $A$ and $B$ where the area of cross section are $40 \mathrm{~cm}^{2}$ and $20 \mathrm{~cm}^{2}$, respectively. Find the rate of flow of water through the tube.
(density of water $=1000 \mathrm{kgm}^{-3}$ )
Correct Option: , 2
(2) According to question, area of cross-section at $A, a A$ $=40 \mathrm{~cm}^{2}$ and at $B, a B=20 \mathrm{~cm}^{2}$
Let velocity of liquid flow at $A,=V_{A}$ and at $B,=V_{B}$ Using equation of continuity $a_{A} V_{A}=a_{B} V_{B}$
$40 V_{A}=20 V_{B}$
$\Rightarrow \quad 2 V_{A}=V_{B}$
Now, using Bernoulli's equation
$P_{A}+\frac{1}{2} \rho V_{A}^{2}=P_{B}+\frac{1}{2} \rho V_{B}^{2} \Rightarrow P_{A}-P_{B}=\frac{1}{2} \rho\left(V_{B}^{2}-V_{A}^{2}\right)$
$\Rightarrow \Delta P=\frac{1}{2} 1000\left(V_{B}^{2}-\frac{V_{B}^{2}}{4}\right) \Rightarrow \Delta P=500 \times \frac{3 V_{B}^{2}}{4}$
$\Rightarrow V_{B}=\sqrt{\frac{(\Delta P) \times 4}{1500}}=\sqrt{\frac{(700) \times 4}{1500}} \mathrm{~m} / \mathrm{s}=1.37 \times 10^{2} \mathrm{~cm} / \mathrm{s}$
Volume flow rate $\mathrm{Q}=a_{B} \times v_{B}$
$=20 \times 100 \times V_{B}=2732 \mathrm{~cm}^{3} / \mathrm{s} \approx 2720 \mathrm{~cm}^{3} / \mathrm{s}$
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