Calculate Speed of Water Flowing from Perforation in Spray Gun

To find the speed at which the water flows out from each perforation, we use the Equation of Continuity for an incompressible fluid:

$A_1 v_1 = A_2 v_2$

where:

• $A_1$ is the cross-sectional area of the hose,
• $v_1$ is the speed of water in the hose,
• $A_2$ is the total effective exit area of all perforations combined,
• $v_2$ is the speed of water flowing out from each perforation.

1. Identify the given values:

• Area of the hose: $A_1 = 30 \text{ cm}^2 = 30 \times 10^{-4} \text{ m}^2$
• Speed of water in the hose: $v_1 = 50 \text{ cm/s} = 0.5 \text{ m/s}$
• Number of perforations: $n = 10$
• Area of each perforation: $a = 15 \text{ mm}^2 = 15 \times 10^{-6} \text{ m}^2$

2. Calculate the total exit area ($A_2$):

$A_2 = n \times a$ $A_2 = 10 \times (15 \times 10^{-6} \text{ m}^2) = 150 \times 10^{-6} \text{ m}^2 = 1.5 \times 10^{-4} \text{ m}^2$

3. Apply the Equation of Continuity:

$A_1 v_1 = A_2 v_2$

Substitute the values into the equation: $(30 \times 10^{-4} \text{ m}^2) \times 0.5 \text{ m/s} = (1.5 \times 10^{-4} \text{ m}^2) \times v_2$

Solve for $v_2$: $v_2 = \frac{30 \times 10^{-4} \times 0.5}{1.5 \times 10^{-4}}$

$v_2 = \frac{15 \times 10^{-4}}{1.5 \times 10^{-4}} = 10 \text{ m/s}$

Thus, the speed at which water flows out from each perforation is $10\text{ m/s}$.

Correct Answer: B ($10\text{ m/s}$)