Question

At the bottom of the lake the pressure is 1.5 atmosphere . What is the depth of the lake? (1 atm= 10 to the power 5 Pa)​

Answer 1

Answer:

Explanation:

Depth = d

Atmospheric Pressure = P₀ = 10⁵ Pa

Density of water at 4°C (ρ) = 10³ kg/m³

Pressure at half of depth

P = P₀ + (d/2)ρg

P = P₀ + 0.5dρg

Pressure at the bottom of lake

P’ = P₀ + dρg

Given that P = 2P’/3

P₀ + 0.5dρg = 2(P₀ + dρg)/3

P₀ + 0.5dg = 2P₀/3 + 2dρg/3

P₀/3 = dρg/6

d = 2P₀ / (ρg)

d = (2 × 10⁵ Pa) / (10³ kg/m³ × 10 m/s²)

d = 20 m

Depth of lake is 20 m

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Answer 2

Depth = d

Atmospheric Pressure = P₀ = 10⁵ Pa

Density of water at 4°C (ρ) = 10³ kg/m³

Pressure at half of depth

P = P₀ + (d/2)ρg

P = P₀ + 0.5dρg

Pressure at the bottom of lake

P’ = P₀ + dρg

Given that P = 2P’/3

P₀ + 0.5dρg = 2(P₀ + dρg)/3

P₀ + 0.5dg = 2P₀/3 + 2dρg/3

P₀/3 = dρg/6

d = 2P₀ / (ρg)

d = (2 × 10⁵ Pa) / (10³ kg/m³ × 10 m/s²)

d = 20 m

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