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Chapter 14: Q. 5 (page 384)

A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?

Short Answer

Expert verified

The mass of liquid is 2435 kg

Step by step solution

01

Given information

Diameter of vat = 1 m

so radius = 0.5 m

depth of liquid = 2.0 m.

The pressure at the bottom of the vat = 1.3 atm.

02

Explanation

Total pressure is calculated by

PTotal = Patm + hρg

PTotal = pressure at the bottom = 1.3 atm

Patm = atmospheric pressure = atm

h = depth of liquid = 2 m

ρ= density of liquid

g = gravitational acceleration

As given

PTotal = Patm + hρg = 1.3 atm

So, hρg = 0.3 atm

Substitute the value and find density

ρ=Phg=(30397.5bar)(2m)×(9.8m/s2)=1551kg·m-3

From basic mensuration find the volume of liquid

V=πr2h=3.14×(0.5m)2×(2m)=1.57m3

Now find the mass using Mass = Volume x Density

M=V×ρ=1.57m3×1551kg/m3=2435kg

So the mass of liquid is 2435 kg.

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