Question

Use the pressure meter to read the pressure in Fluid A at the bottom of the tank. Do not move the pressure meter. Switch to Fluid B and read the pressure in fluid B. Based on the two readings, compare the density of fluid B to the density of fluid A. Which statement is correct?

Answer 1

`P_b = (\rho_b)/(\rho_a) \ P_a`

Step-by-step explanation:

The pressure at a depth of a fluid is

P = ρ g y

where ρ is the density of the fluid, y the depth of the gauge measured from the surface of the fluid.

In this case the pressure for fluid A is

Pa = ρₐ g y

the pressure for fluid B is

P_b = ρ_b g y

depth y not changes as the gauge is stationary

if we look for the relationship between these pressures

`(P_a)/(P_b) = ( \rho_a)/(\rho_b)`

`P_b = (\rho_b)/(\rho_a) \ P_a`

therefore we see that the pressure measured for fluid B is different from the pressure of fluid A

if ρₐ < ρ_b B the pressure P_b is greater than the initial reading

ρₐ> ρ_b the pressure in B decreases with respect to the reading in liquid A