(B) According to the equation of continuity for an incompressible fluid,the volume flow rate remains constant: $A_1 v_1 = N A_2 v_2$.Here,$A_1 = 30 \t

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(B) According to the equation of continuity for an incompressible fluid,the volume flow rate remains constant: $A_1 v_1 = N A_2 v_2$.Here,$A_1 = 30 \text{ cm}^2 = 3000 \text{ mm}^2$,$v_1 = 50 \text{ cm/s}$,$N = 10$,and $A_2 = 15 \text{ mm}^2$.Substituting the values: $3000 \text{ mm}^2 \times 50 \text{ cm/s} = 10 \times 15 \text{ mm}^2 \times v_2$.$150000 \text{ mm}^2 \cdot \text{cm/s} = 150 \text{ mm}^2 \times v_2$.$v_2 = \frac{150000}{150} \text{ cm/s} = 1000 \text{ cm/s}$.Converting to $SI$ units: $v_2 = 1000 \text{ cm/s} = 10 \text{ m/s}$.

Class 11 Physics Fluid Mechanics and Surface Tension Types of Flow, Equation of Continuity and Flow Rate

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$A$ water spray gun is attached to a hose of cross-sectional area $30 \text{ cm}^2$. The gun comprises $10$ perforations,each of cross-sectional area $15 \text{ mm}^2$. If the water flows in the hose with a speed of $50 \text{ cm/s}$,calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

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A
$100 \text{ m/s}$
B
$10 \text{ m/s}$
C
$1000 \text{ m/s}$
D
$15 \times 10^2 \text{ m/s}$

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Fluid Mechanics and Surface Tension

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Types of Flow, Equation of Continuity and Flow Rate

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