# What is the mass of the liquid in the vat?

What is the mass of the liquid in the vat?

A 0.60-m-diameter vat of liquid is 2.7m deep. The pressure at the bottom of the vat is 1.5atm .

I tried this problem using the formula P=P_0+(rho)gd and replacing the density (rho) with mass/ volume and solving for mass that way. I used 151,987.5 Pa (equal to 1.5 atm) for P and I assumed P_0 to be 101,325 Pa (equal to 1atm), although I think this assumption may be incorrect. I ended up with the wrong answer, and I think it is because I am not sure what to plug in for the pressures. If someone could show me how they would correctly solve this problem I’d really appreciate it. Thanks!!

Get the volume and use the pressure to determine the density.

What is missing is the pressure is absolute or relative. I’ll assume absolute.

V = πr²h = π(0.3)²(2.7) = 0.763 m³

Pfluid = ρgh

Pfluid is pressure in Pa or N/m²

ρ is the density of the fluid in kg/m³

g is the acceleration of gravity 9.8 m/s²

h is the height of the fluid above the object in m

1.5 atm is 1.5•101 kPa

ρ = P/gh = (151.5e3) / (9.8)(2.7) = 5726 kg/m³

(possibly molten tin)

5726 kg/m³ x 0.763 m³ = 4370 kg

What is the mass of the liquid in the vat?

Categories d