Question

Water is flowing through a channel that is $12 \, m$ wide with a speed of $0.75 \, m \, s^{- 1}$ . The water then flows into four identical channels that have a width of $4.0 \, m$ each. The depth of the water does not change as it flows into the four channels. The speed of the water in one of the smaller channels is

• A. $0.56 \, ms^{- 1}$
• B. $2.3 \, ms^{- 1}$
• C. $0.25 \, ms^{- 1}$
• D. $0.75 \, ms^{- 1}$

Answer 1

Answer: (A)

$Av \, = \, A_{1}v_{1} \, + \, A_{2}v_{2} \, + \, A_{3}v_{3} \, + \, A_{4}v_{4}$
$Av \, = \, 4\left(\right.A_{1}v_{1}\left.\right)$
$12 \, \times \, 0.75 \, = \, 4 \, \left[\right.4 \, \times \, v\left]\right.$
$v= \, \frac{3}{4}\times \, 0.75$
$= \, 0.75 \, \times \, 0.75$
$v=\text{0.56}\,ms^{- 1}$