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.
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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
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