Question 17: Properties of Matter

Question

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

Accepted Answer

Use the equation of continuity:
$$ A_1 v_1 = A_2 v_2 $$
Here,
area of hose, $A_1 = 30 \,	ext{cm}^2$
speed of water in hose, $v_1 = 50 \,	ext{cm/s}$
Now the spray gun has 10 perforations, each of area
$$ 15 \,	ext{mm}^2 $$
So total outlet area is
$$ A_2 = 10 	imes 15 = 150 \,	ext{mm}^2 $$
Convert this into $	ext{cm}^2$:
Since
$$ 1 \,	ext{cm}^2 = 100 \,	ext{mm}^2 $$
therefore,
$$ 150 \,	ext{mm}^2 = \frac{150}{100} = 1.5 \,	ext{cm}^2 $$
Now apply continuity equation:
$$ 30 	imes 50 = 1.5 	imes v_2 $$
$$ v_2 = \frac{30 	imes 50}{1.5} $$
$$ v_2 = 1000 \,	ext{cm/s} $$
Convert into $	ext{m/s}$:
$$ 1000 \,	ext{cm/s} = 10 \,	ext{m/s} $$
So, the speed of water from each perforation is
$$ \boxed{10 \,	ext{m/s}} $$
Correct option: B

Answer

$100 \mathrm{~m} / \mathrm{s}$

Answer

$10 \mathrm{~m} / \mathrm{s}$

Answer

$1000 \mathrm{~m} / \mathrm{s}$

Answer

$15 	imes 10^2 \mathrm{~m} / \mathrm{s}$

Properties of Matter

Choose the correct answer: