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 ratio 1:2:3. Assuming streamline flow, the ratio of the speed of ganga to that of the alaknanda is​

Answer 1

Given : 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 ratio 1:2:3.

To find : the ratio of the speed of ganga to that of the alaknanda

Solution:

Let Bhagirath Speed  =  2S

Then Alaknanda Speed =  3S

Cross section area of  Bhagirath = A

Cross section area of  Alaknanda = 2A

Cross section area of  Ganga  = 3A

Volume flow rate of  Bhagirath   = 2S * A    = 2AS

Volume flow rate of  Alaknanda    =3S * 2A   = 6AS

Volume flow rate of  Ganga  = 2AS + 6AS = 8AS

=> Speed of Ganga   = 8AS/3A

=>  Speed of Ganga   =  8S/3

ratio of the speed of ganga to that of the alaknanda

8S/3  : 3S

=  8S : 9S

= 8 : 9

8 : 9   is the ratio of the speed of ganga to that of the alaknanda

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