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Liquid of density rho flows along a hori...

Liquid of density `rho` flows along a horizontal pipe of uniform area of cross section a with a velocity v through a right angled bend. What force should be applied to the bend to hold it in equilibrium?

Text Solution

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Change in momentum of mass `Deltam` of liquid as it passes through the bend

`Deltap =P_(f)-P_(i)`
`=Deltamv sqrt(2)`
`F =(DeltaP)/(Deltat) = sqrt(2) xx (Deltam)/(Deltat)`, [as `Deltam = rho ADeltaL`]
`F=sqrt(2)v(rho.ADeltaL)/(Deltat)`, [as `DeltaL//Deltat=v`]
`F=sqrt(2)rhoAv^(2)`
So the force to be applied at the bend to hold it in position is`sqrt(2)rhoAv^(2)` in the direction as shown in fig. (Otherwise pipe will move in opposite direction.)
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