At a certain confluence, river Yamuna mixes with the river Chambal and becomes river Kaveri. Suppose Yamuna has a width of 12 m , Chambal has a width of 8 m and Kaveri has a width of 16 m . Assume that the depth of

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Quantrex Academy · Accepted Answer

Correct answer: A. 23 km h^ -1

According to the equation of continuity, the total volume flow rate of water before the confluence is equal to the volume flow rate after the confluence.

Q_{Kaveri} = Q_{Yamuna} + Q_{Chambal}

A_K v_K = A_Y v_Y + A_C v_C

Since the depth

d

is identical in all three rivers, the cross-sectional area is given by

A = w \times d

, where

w

is the width.

w_K d v_K = w_Y d v_Y + w_C d v_C

Dividing by

d

gives:

w_K v_K = w_Y v_Y + w_C v_C

Substituting the given values:

16 \times v_K = 12 \times 20 + 8 \times 16

16 v_K = 240 + 128

16 v_K = 368

v_K = \dfrac{368}{16} = 23 \text{ km h}^{-1}

At a certain confluence, river Yamuna mixes with the river Chambal...

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