Question

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

Answer 1

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.

Now, we have to equate pressures on both sides to get our desired ratio, thus P_0 + rho A g(3h + h) = P_0 + rho B g(h) P_0 is the atmospheric pressure, by cancelling it out from both sides we get 4 rho A gh = rho B gh or 4 rho A = rho B and rho B/rho A = 4/1 Hence, we can clearly say that the liquid B has higher density than A (exactly 4 times higher)

Now,

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

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

P_o 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)