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  4. At Deoprayag in Garhwal (Uttarakhand), river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Assume that Alaknanda, Bhagirathi and Ganga have widths 12 m , 8 m and 16 m respectively. Again, assume that the average speeds of water in Alaknanda and Bhagirathi are 20 km h -1 and 16 km h -1 respectively. Then, the average speed of water in the river Ganga is [Depth same in each case]

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Q. At Deoprayag in Garhwal (Uttarakhand), river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Assume that Alaknanda, Bhagirathi and Ganga have widths 12 m , 8 m and 16 m respectively. Again, assume that the average speeds of water in Alaknanda and Bhagirathi are $20 \,km \,h ^{-1}$ and $16 \,km \,h ^{-1}$ respectively. Then, the average speed of water in the river Ganga is [Depth same in each case]

Mechanical Properties of Fluids

Solution:

Equation of continuity gives,
$A_{a} v_{a}+A_{b} v_{b}=A_{g} v_{g}$
Let the depths be $d$ for each.
$(12 d)(20)+(8 d)(16)=(16 d) \cdot v$
$240+128=16 v$
$v=\frac{368}{16}$
$=23 \,km \,hr ^{-1}$