The Bhagirathi and the Alaknanda merge at Deo | vedclass

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Question

(C) Since water is not stored anywhere,the volume flow rate of the Ganga must equal the sum of the volume flow rates of the Bhagirathi and the Alaknan

Vedclass · Accepted Answer

$8: 9$

Vedclass · Answer

(C) Since water is not stored anywhere,the volume flow rate of the Ganga must equal the sum of the volume flow rates of the Bhagirathi and the Alaknanda.By the equation of continuity,we have:$A_g v_g = A_b v_b + A_a v_a \quad \dots(i)$Given the ratio of cross-sectional areas $A_b : A_a : A_g = 1 : 2 : 3$,we can write:$A_b = x, A_a = 2x, A_g = 3x$Given the ratio of speeds $v_b : v_a = 1 : 1.5 = 1 : \frac{3}{2}$,we can write:$v_b = y, v_a = 1.5y = \frac{3}{2}y$Substituting these values into equation $(i)$:$3x \cdot v_g = x \cdot y + 2x \cdot \left(\frac{3}{2}yight)$$3x \cdot v_g = xy + 3xy = 4xy$$v_g = \frac{4}{3}y$Now,the ratio of the speed of the Ganga to that of the Alaknanda is:$\frac{v_g}{v_a} = \frac{\frac{4}{3}y}{\frac{3}{2}y} = \frac{4}{3} 	imes \frac{2}{3} = \frac{8}{9}$

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