Question

The Bhagirathi and the Alaknanda merge at Deoprayag to form the Ganga with their speeds in the ratio 1 : 1 : 5. The cross-sectional areas of the Bhagirathi, the Alaknanda and the Ganga are in the ratio 1 : 2 : 3. Assuming streamline flow, the ratio of the speed of Ganga to that of the Alaknanda is

(a) 7 : 9

(b) 4 : 3

(c) 8 : 9

(d) 5 : 3

Answer 1

Answer is : (c) 8 : 9

As water is not stored anywhere. So, volume flow rate of Ganga = volume flow rate of Bhagirathi + volume flow rate of Alaknand

∴ By equation of continuity, we have

It is given that area of flow of Ganga, Alaknanda and Bhagirathi are in ratio,

Also, ratio of speeds of Bhagirathi and Alaknanda is

Substituting these values in Eq. (i), we get

∴ Ratio of speed of Ganga to that of Alaknanda is