Find the height of the water column that will exert the pressure equal to 1 bar. (Take density of water = 1000 kg/m³ and g = 10 m/sec²)

CONCEPT:

Pressure:

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

• 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 = 1 bar = 105 Pa, 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,

⇒ P = ρgh

⇒ 105 = 1000 × 10 × h

⇒ h = 10 m

• Hence, option 2 is correct.