Water flows in a horizontal tube (see figure). The pressure of wa… - Vidyadip

MCQ

Water flows in a horizontal tube (see figure). The pressure of water changes by $700\; \mathrm{Nm}^{-2}$ between $\mathrm{A}$ and $\mathrm{B}$ 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. ........ $\mathrm{cm}^{3} / \mathrm{s}$

(density of water $=1000\; \mathrm{kgm}^{-3}$ )

A
$1810$
B
$3020 $
✓
$2720 $
D
$2420$

✓

Answer

Correct option: C.

$2720 $

c
Rate of flow of water $=\mathrm{A}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}=\mathrm{A}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}$

$(40) \mathrm{V}_{\mathrm{A}}=(20) \mathrm{V}_{\mathrm{B}}$

$\mathrm{V}_{\mathrm{B}}=2 \mathrm{V}_{\mathrm{A}}$

Using Bernoulli's theorem

$\mathrm{P}_{\mathrm{A}}+\frac{1}{2} \rho \mathrm{V}_{\mathrm{A}}^{2}=\mathrm{P}_{\mathrm{B}}+\frac{1}{2} \rho \mathrm{V}_{\mathrm{B}}^{2}$

$\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}=\frac{1}{2} \rho\left(\mathrm{V}_{\mathrm{B}}^{2}-\mathrm{V}_{\mathrm{A}}^{2}\right)$

$700=\frac{1}{2} \times 1000\left(4 \mathrm{V}_{\mathrm{A}}^{2}-\mathrm{V}_{\mathrm{A}}^{2}\right)$

$\mathrm{V}_{\mathrm{A}}=0.68 \mathrm{m} / \mathrm{s}=68 \mathrm{cm} / \mathrm{s}$

Rate of flow $=\mathrm{A}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}$

$=(40)(68)=2720\; \mathrm{cm}^{3} / \mathrm{s}$

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