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R 5. Equal volumes of two fluids are added to the U-shaped pipe as shown in...

Question

R 5. Equal volumes of two fluids are added to the U-shaped pipe as shown in...

r 5. Equal volumes of two fluids are added to the U-shaped pipe as shown in Figure CQ9.5. The pipe is open at both ends and the fluids come to equilibrium without mixing. (a) Which fluicd has the higher density, fluid A or fluid B? (b) What is the ratio PB/PA of the fluid densities? 3h h B Figure Ca9.5
r 5. Equal volumes of two fluids are added to the U-shaped pipe as shown in Figure CQ9.5. The pipe is open at both ends and the fluids come to equilibrium without mixing. (a) Which fluicd has the higher density, fluid A or fluid B? (b) What is the ratio PB/PA of the fluid densities? 3h h B Figure Ca9.5

Answers

Pressure at a point P and Q in both sides of the U shaped tube 4h heigth from above will be same. Points are shown in the figure below.

3h Point Q Point P

Now,

we have to equate pressures on both sides to get our desired ratio, thus

P_o + \rho _A g (3h+h) = P_o + \rho _B g(h)

Po is the atmospheric pressure , by cancelling it out from both sides we get

4 \rho _A g h = \rho _B g h

or

4 \rho _A = \rho _B

and

\frac{\rho _B }{\rho _A } = \frac{4}{1}

Hence, we can clearly say that the liquid B has higher density than liquid A (exactly 4 times higher)


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