Question

At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of 12 m, Bhagirathi has a width of 8 m and Ganga has a width of 16 m. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be 20 km h^-1 and in Bhagirathi be 16 km h^-1. Find the average speed of water in the river Ganga.

• A. 46 km/hr
• B. 23 m/s
• C. 23 km/hr
• D. 46 m/s

Answer 1

The correct option is C

23 km/hr

The situation is depicted as shown,

Let the depth of all three rivers be 'D' m

As the water flowing per unit time in river Ganga should be equal to the sum of water flowing in Alaknanda and Bhagirathi per unit time as the volume flow rate should be constant.
$\Rightarrow A_1{V}_1+A_2{V}_2=A_3{V}_3$
$(H\times 12\times 20)+(H\times 8\times 16)=(16\times H\times V_G)$
$\Rightarrow V_G=23\frac{km}{hr}$