Question

At Deoprayag (Garwal, UP) river Alaknande 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

Given:
Average speed of water in Alaknanda = 20 kmh⁻¹
Average speed of water in Bhagirathi = 16 kmh⁻¹
Width of Bhagirathi = 8 m
Width of Alaknanda = 12 m
Width of Ganga = 16 m
Now,
Volume of water discharged from Alaknanda + Volume of water discharged from Bhagirathi = Volume of water flow in Ganga
Let:
d = Depth of the three rivers
⇒V_A × d × 12 + V_B × d × 8 = V_G × d × 16
Here, V_A, V_B and V_G be the average speeds of water in Alaknanda, Bhagirathi and Ganga, respectively.
Using the equation of continuity, we get: 

\[20 \times 12 + 16 \times 8 = V_G \times 16\]
\[ \Rightarrow V_G \times 16 = 368\]
\[ \Rightarrow V_G = \frac{368}{16}\]
\[ = 23 \text{km/h}\]