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A liquid of density p flows along a horizontal pipe of uniform cross - section A with a velocity v through a right angled bend as shown in fig. What force has to be exerted at the bend to hold the pipe in equilibrium? |
Answer» Solution :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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