Question:medium
A water spray gun is attached to a hose of cross sectional area $30 \text{ cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \text{ mm}^2$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)
A water spray gun is attached to a hose of cross sectional area $30 \text{ cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \text{ mm}^2$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)
Updated On: Oct 9, 2026
- 100 m/s
- 10 m/s
- 1000 m/s
- $15 \times 10^2$ m/s
Show Solution
The Correct Option is B
Solution and Explanation
Step 1: Use continuity equation
\[ A_1v_1=nA_2v_2 \] Step 2: Convert units
\[ A_1=30\,\text{cm}^2=30\times 10^{-4}\,\text{m}^2 \] \[ v_1=50\,\text{cm/s}=0.5\,\text{m/s} \] \[ A_2=15\,\text{mm}^2=15\times 10^{-6}\,\text{m}^2 \] \[ n=10 \] Step 3: Find exit velocity
\[ v_2=\frac{A_1v_1}{nA_2} \] \[ = \frac{(30\times 10^{-4})(0.5)} {10(15\times 10^{-6})} \] \[ = \frac{15\times 10^{-4}} {15\times 10^{-5}} \] \[ =10 \] \[ v_2=10\,\text{m/s} \] Final Answer: \[ \boxed{10\,\text{m/s}} \]
\[ A_1v_1=nA_2v_2 \] Step 2: Convert units
\[ A_1=30\,\text{cm}^2=30\times 10^{-4}\,\text{m}^2 \] \[ v_1=50\,\text{cm/s}=0.5\,\text{m/s} \] \[ A_2=15\,\text{mm}^2=15\times 10^{-6}\,\text{m}^2 \] \[ n=10 \] Step 3: Find exit velocity
\[ v_2=\frac{A_1v_1}{nA_2} \] \[ = \frac{(30\times 10^{-4})(0.5)} {10(15\times 10^{-6})} \] \[ = \frac{15\times 10^{-4}} {15\times 10^{-5}} \] \[ =10 \] \[ v_2=10\,\text{m/s} \] Final Answer: \[ \boxed{10\,\text{m/s}} \]
Was this answer helpful?
0
