Question 193: Properties of Matter

Question

Water is flowing continuously from a tap having an internal diameter $$8 	imes {10^{ - 3}}\,\,m.$$ The water velocity as it leaves the tap is $$0.4\,\,m{s^{ - 1}}$$ . The diameter of the water stream at a distance $$2 	imes {10^{ - 1}}\,\,m$$ below the tap is close to :

Accepted Answer

From Bernoulli's theorem,
$${P_0} + {1 \over 2}ho v_1^2ho gh = {P_0} + {1 \over 2}ho v_2^2 + 0$$
$${v_2} = \sqrt {v_1^2 + 2gh} $$
$$ = \sqrt {0.16 + 2 	imes 10 	imes 0.2} $$
$$ = 2.03\,m/s$$
From equation of continuity
$${A_2}{v_2} = {A_1}{v_1}$$
$$\pi {{D_2^2} \over 4} 	imes {v_2} = \pi {{D_1^2} \over 4}{v_1}$$
$$ \Rightarrow \,\,{D_1} = {D_2}\sqrt {{{{v_1}} \over {{v_2}}}}  = 3.55 	imes {10^{ - 3}}m$$

Answer

$$7.5 	imes {10^{ - 3}}m$$

Answer

$$9.6 	imes {10^{ - 3}}m$$

Answer

$$3.6 	imes {10^{ - 3}}m$$

Answer

$$5.0 	imes {10^{ - 3}}m$$

Properties of Matter

Water is flowing continuously from a tap having an internal diameter $8 \times {10^{ - 3}}\,\,m. The water velocity as it leaves the tap is 0.4\,\,m{s^{ - 1}} . The diameter of the water stream at a distance 2 \times {10^{ - 1}}\,\,m$ below the tap is close to :

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