Question

(a) How high in meters must a column of water be to exert a pressure equal to that of a 760-mm column of mercury? The density of water is 1.0 g/mL whereas that of mercury is 13.6 g/mL (b) What is the pressure, in atmospheres, on the body of a diver if he or she is 39 ft below the surface of the water when atmospheric pressure at the surface is 0.97 atm?

Answer 1

(a)

Pressure of a liquid at the bottom is related to its height as :

P = d*g*h

Here d is density of the liquid

For pressure of water and mercury to be equal, we have :

P₁ = P₂

d₁*g*h₁ = d₂*g*h₂

Here , d₁ = density of water = 1 g/mL, d₂ = density of mercury = 13.6 g/mL, h₂ = 760 mm

Thus, d₁ = 13.6*760/1 = 10336 mm = 10.336 m

(b)

Pressure at 39 ft depth = Pressure due to atmosphere + Pressure due to water

Pressure due to water, P_w = d*g*h

Here, d = 1000 kg/m³ , g = 9.81 m/s², h = 39 ft = 11.8872 m

Thus, P_w = 1000*9.81*11.8872 = 116613.432 Pa = 1.15 atm

Thus, total pressure = 0.97 + 1.15 = 2.12 atm

Answer 2

a)

We know P=h(rho)g

so 1atm=760*13.6*g=h*1*g

=>h = 10336mm or 10.336mts

b)

1 ft = 0.3048 m

39fts = 11.8872mts

so pressure = 11.8872/10.336 = 1.150077399380805atm

so pressure on the person = 2.12 atm