Question

a. What volume of water has the same mass as 8.0 m³ of ethyl alcohol?
b. If this volume of water is in a cubic tank, what is the pressure at the bottom?

Short answer

a) Volume is 6.312 m³

b) Pressure is 18 kPa

Step-by-step solution

Part(a) Step1: Given Information

Vol 8.0 m³of ethyl alcohol is 8.0 m³

Part(a) Step2 : Explanation

Volume can be calculated as V = M/ρ

First calculate mass of ethyl alcohol , then use that mass to calculate volume of water

Mass of ethyl alcohol = M_e = V x ρ_e

ρ_e = density of ethyl alcohol = 789 kg/m³

V = 8 m³

M_e = 8 x 789 kg/m³ = 6312 kg.

Now find the volume of the water

V_w = M/ρ_w = $\frac{6312kg}{1000kg/m^3}=6.312m^3$

Part(b) Step 1 : given information

The volume of water in part(a) is filled in a cubic tank,

Explanation

First find the dimension of the cubic tank for a volume 6.312 m³

The side of a cube is

$a=\sqrt[3]{6.312}=1.85m$

Now find the pressure exerted

$\text{pressure}P=h\rho g=1.85\times 1000\times 9.8=18\mathrm{kPa}$

Pressure exerted is 18 kPa.