Suppose a liquid level from 5.5 to 8.6 m is linearly converted to pneumatic pressure from 3 to 15 psi. What pressure will result from a level of 7.2 m? What level does a pressure of 4.7 psi represent?

a) P = 9.58 psi for h=7.2 m

b) P=4.7 psi for h=5.94 m

Explanation:

Since the pressure Pon a static liquid level h is

P = p₀ + ρ*g*h

where p₀ = initial pressure, ρ=density, g = gravity

then he variation of the liquid level Δh will produce a variation of pressure of

ΔP = ρ*g*Δh → ΔP/Δh = ρ*g = (15 psi - 3 psi) / (8.6 m - 5.5 m) = 12/3.1 psi/m

if the liquid level is converted linearly

P = P₁ + ΔP/Δh * (h - h₁)

therefore choosing P₁ = 3 psi and h₁ = 5.5 m, for h=7.2 m

P = 3 psi + 12/3.1 psi/m * (7.2 m - 5.5 m) = 9.58 psi

then P = 9.58 psi for h=7.2 m

for P=4.7 psi

4.7 psi = 3 psi + 12/3.1 psi/m * (h - 5.5 m)

h = (4.7 psi - 3 psi) / (12/3.1 psi/m) + 5.5 m = 5.94 m

then P=4.7 psi for h=5.94 m