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]

Question

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] (A) 21 km h -1 (B) 23 km h -1 (C) 25 km h -1 (D) 27 km h -1

Tardigrade Admin · Accepted Answer

Equation of continuity gives, Aa va+Ab vb=Ag vg Let the depths be d for each. (12 d)(20)+(8 d)(16)=(16 d) ⋅ v 240+128=16 v v=(368/16) =23 km hr -1

$21 km h^{- 1}$

$23 km h^{- 1}$

$25 km h^{- 1}$

$27 km h^{- 1}$

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

21kmh−1

23kmh−1

25kmh−1

27kmh−1

Equation of continuity gives, Aa​va​+Ab​vb​=Ag​vg​ Let the depths be d for each. (12d)(20)+(8d)(16)=(16d)⋅v 240+128=16v v=16368​ =23kmhr−1

$21 km h^{- 1}$

$23 km h^{- 1}$

$25 km h^{- 1}$

$27 km h^{- 1}$

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