What is the mass of the liquid in the vat?

Question

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!!

Sarai Dooley Jr. · Accepted Answer

p=p0+ρghthenρ=(p-p0)/(gh)1 atm=101,325 Paρ=(1.5-1)*101,325/(9.8*2.7) ρ=1914.7 kg/m^3m=ρVV=0.76 m^3m=1914.7*0.76=1455.2 kg

Sarai Dooley Jr. · Answer

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 m³Pfluid = 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 kPaρ = P/gh = (151.5e3) / (9.8)(2.7) = 5726 kg/m³(possibly molten tin)5726 kg/m³ x 0.763 m³ = 4370 kg

Sarai Dooley Jr. · Answer

the pressure times the area of the bottom of the vat = the total force of gravity on the massthis is a snap to calculate

Dr. Karlee Tillman

What is the mass of the liquid in the vat?

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