A liquid of density 600 flowing steadily in a tube of varying cross-section. The cross-section at a point A is

Question

A liquid of density 600 $kg / m^{3}$ flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 ${cm}^{2}$ and that at B is 20 ${mm}^{2}$ . Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm/s. The difference in pressures at A and B points is ______ Pa. [2026]

Smart Achievers · Accepted Answer

(4)

$Using continuity equation,$

${cm}^{2}$

$1 \times 10 = 0.2 \times V_{B}$

$\Rightarrow V_{B} = 50 cm/s = 0.5 m/s$

$P_{A} + \frac{1}{2} ρ v_{A}^{2} = P_{B} + \frac{1}{2} ρ v_{B}^{2}$

$P_{A} - P_{B} = \frac{1}{2} ρ (v_{B}^{2} - v_{A}^{2})$

$P_{A} - P_{B} = \frac{1}{2} \times 600 \times ({(0.5)}^{2} - {(0.1)}^{2})$

$\Rightarrow P_{A} - P_{B} = 72$

Solution

1 18

2 144

3 36

4 72

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