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 water is identical in all three rivers. If the average speed of water in Yamuna is 20 km h ⁻¹ and in Chambal is 16 km h ⁻¹ , determine the average speed of water in the river Kaveri.

Step-by-step solution

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 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 v_K = 12 20 + 8 16 16 v_K = 240 + 128 16 v_K = 368 v_K = 368 16 =