A river gradually deepens from a depth of 4 | vedclass

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(C) According to the equation of continuity for an incompressible fluid,the product of the cross-sectional area and the velocity remains constant,i.e.

Vedclass · Accepted Answer

$6$

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(C) According to the equation of continuity for an incompressible fluid,the product of the cross-sectional area and the velocity remains constant,i.e.,$A_{1}v_{1} = A_{2}v_{2}$.Here,the cross-sectional area $A$ is given by the product of width $W$ and depth $d$. Since the width $W$ is constant,we have:$A_{1} = W 	imes 4 \ m$$A_{2} = W 	imes 8 \ m$Given $v_{1} = 12 \ m/s$,we substitute these values into the continuity equation:$(W 	imes 4) 	imes 12 = (W 	imes 8) 	imes v_{2}$Dividing both sides by $W$ (since $W 
eq 0$):$4 	imes 12 = 8 	imes v_{2}$$48 = 8 	imes v_{2}$$v_{2} = \frac{48}{8} = 6 \ m/s$.Thus,the velocity at the $8 \ m$ depth is $6 \ m/s$.

$A$ river gradually deepens from a depth of $4 \ m$ to a depth of $8 \ m$ as shown. The width,$W$,of the river does not change. At the depth of $4 \ m$,the river's speed is $12 \ m/s$. Its velocity at the $8 \ m$ depth is ......... $m/s$.

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