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 and in Bhagirathi be 16 km/h. Find the average speed of water in the river Ganga.

Answer 1

If the average depth of rivers is h meter, then the flow  volume of water in the river Alaknanda =20*h*12000/3600 m³/s 

=66.67h m³/s

 The flow volume of water in the river Bhagirathi =8*h*16000/3600 m³/s 

=35.56h m³/s 

Total flow volume in the rivers before mixing  

=66.67h + 35.56h =102.23h m³/s 

If the average speed in the river Ganga be V km/h, then flow volume 

=16*h*V*1000/3600 m³/s =4.44hV m³/s 

This would be equal to the flow volume before mixing, 

so 4.44hV =102.23h 

→V = 102.23/4.44 

=23 km/h

Answer 2

Volume of water, discharged from Alkananda + vol are of water discharged from Bhagirathi = Volume of water flow in Ganga.