Solve the problem

Question

The pressure at a depth of well is three times the pressure at a depth of 2 m. Calculate the depth of the well if the atmospheric pressure is 10.33m of water column

Answer 1

g = acceleration of gravity

ρ = density of water

p₀ = atmospheric pressure

d₁ = depth of 2m

p₁ = pressure at depth d₁

d₂ = depth where pressure is 3p₁ 

p₂ = 3p₁

 

p₁ = p₀ + ρgd₁ 

p₂ = p₀ + ρgd₂ = 3p₁ ⇒

 

d₂ = (3p₁ - p₀)/(ρg)

 

d₂ = [3(p₀ + ρgd₁) - p₀]/(ρg)

 

d₂ = (3ρgd₁ + 2p₀)/(ρg)

 

You know ρ, g, d₁, and p₀.  Now plug in the numbers in appropriate units and finish from here.