Water flows through a horizontal tube of variable cross section. The cross-sectional areas at A and B are 4 mm^2 and 2 mm^2 respectively. Given that 1 cc of water enters through A per second, compute the speed of the

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Correct answer: D. 50 cm/s

According to the equation of continuity, the volume flow rate

Q

remains constant throughout the tube.

Q = A_A v_A = A_B v_B

Given, the volume of water entering per second at

A

is

Q = 1 \text{ cc/s} = 1 \text{ cm}^3\text{/s}

.

The cross-sectional area at

B

is

A_B = 2 \text{ mm}^2 = 2 \times 10^{-2} \text{ cm}^2

.

The speed of water at

B

is

v_B

.

v_B = \dfrac{Q}{A_B}

v_B = \dfrac{1}{2 \times 10^{-2}} \text{ cm/s}

v_B = \dfrac{100}{2} \text{ cm/s} = 50 \text{ cm/s}

Water flows through a horizontal tube of variable cross section....

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