What is the absolute pressure at a depth of 20 m in a water? (Take atmospheric pressure = 1 bar, g = 10 m/sec², density of water = 1000 kg/m³)

CONCEPT:

Pressure:

• It is defined as the normal force acting per unit area.
• Pressure is a scalar quantity.

⇒ \(P=\frac{F}{{A}}\)

• SI unit of pressure is N/m2 or pascal (Pa).

Variation of pressure with a depth of fluid:

• If the fluid is at rest then the pressure difference between the two points at different levels in the fluid is given as,

⇒ P2 - P1 = ρgh

Where P1 = pressure at point 1, P2 = pressure at point 2, ρ = density of fluid, g = gravitational acceleration, and h = vertical distance between point 1 and point 2

• If point 1 is at the top of the fluid and is open to the atmosphere then,

⇒ P2 = Pa + ρgh

Where Pa = atmospheric pressure

CALCULATION:

Given P_a = 1 bar = 105 Pa, h = 20 m, ρ = 1000 kg/m3 and g = 10 m/sec2

• As we know that the pressure exerted by the fluid column of height h at its bottom is given as,

⇒ P₁ = ρgh

⇒ P₁ = 1000 × 10 × 20

⇒ P1 = 2 × 10⁵ Pa

• So the absolute pressure at a depth of 20 m in water is given as,

⇒ P = P1 + P_a

⇒ P = (2 × 105) + 10⁵

⇒ P = 3 × 105 Pa

• Hence, option 3 is correct.