Question

At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of $12m$, Bhagirathi has a width of $8m$ and Ganga has a width of $16m$. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be $20km{h}^{-1}$ and in Bhagirathi be $16km{h}^{-1}$ Find the average speed of water in the river Ganga.

Answer 1

Let the Depth of each river be h km.

Now, In the Given case, the volume rate of the flow of water will be constant throughout.

This means, Volume rate of the River Alaknanada + Volume Rate of the River Bhagirathi = Volume Rate of the River Ganga.

[This is because, In series connection of Horizontal pipe (here stream of river) the sum of the volume rate equal to the final volume rate flow.]

Volume rate of flow of River Alaknanda = Area of cross section × Velocity of the water in River Alaknanda.

= 12/1000 × h × 20

Similarly,

Volume rate of flow of River Bhagirathi = Area of cross section × Velocity of the water in River Bhagirathi.

= 8/1000 × h × 16

Similarly, Volume rate of flow of River Ganga = Area of cross section × Velocity of the water in River Ganga.

= 16/1000 × h × Velocity

Now, Finally,

16/1000 × h × Velocity = 12/1000 × h × 20 + 8/1000 × h × 16

Cancelling h and 1000 from each side,

16 × Velocity = 12 × 20 + 8 × 16

On Solving, We get, Velocity = 23 km/hr.

Hence, the average velocity of the water in the river Ganga is 23 km/hr.