The formula for pressure under water is P=rhogh , where \rho is the density of water, g is gravity, and h is the height of the water. Given the water pressure, prove that you can calculate the height of the water using h=P/rhog} .

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09-09-2022
Mathematics

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The formula for pressure under water is P=rhogh , where \rho is the density of water, g is gravity, and h is the height of the water. Given the water pressure, prove that you can calculate the height of the water using h=P/rhog} .

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ap8997154 ap8997154 · Answer 1 · 2022-09-14T08:43:06+02:00

Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. The proof for calculating water pressure can be given as shown below.

What is Pressure?

Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. Gauge pressure is the pressure in relation to the surrounding atmosphere. Pressure is expressed using a variety of units.

The formula given for pressure under water is P=ρgh, where ρ is the density of water, g is gravity, and h is the height of the water.

Now, if the fomula is solved for h it can be written as,

P=ρgh

Divide both the sides of the equation by ρg, therefore, we can write,

P/ρg = ρgh/ρg

h = P/ρg

Now, the value of ρ for water and g is 997 kg/m³ and 9.81 m/sec², respectively. Therefore, we can write,

h = P/(ρg)

h = P/(997kg/m³ × 9.81 m/sec²)

Now, just with the pressure known we can calculate the height of the water column.

Hence, proved.

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