The Bhagirathi and the Alaknanda merge at Deo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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}$

Similar Questions

$A$ liquid flows in the tube from left to right as shown in the figure. $A_1$ and $A_2$ are the cross-sections of the portions of the tube as shown. The ratio of speed $\frac{v_1}{v_2}$ will be ..........

Explain the concept of a tube of flow.

What is a tube of flow?

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point where the diameter of the pipe becomes $2 \text{ cm}$ is (in $\text{ m/s}$)

Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\, m$. The water velocity as it leaves the tap is $0.04\, ms^{-1}$. The diameter of the water stream at a distance $8 \times 10^{-1}\, m$ below the tap is close to

Vedclass Test Series

Exam Paper Generator

Online Exam Module