Hydraulic Pressure Equation

Introduction to hydraulic pressure equation

The hydraulic pressure means the pressure exerted due to a liquid column. The pressure of a liquids is defined as the amount of normal force acting per unit area on the surface. Hydraulic pressure is a scalar equation and the unit of hydraulic pressure is Newton per square metre.

Let us assume that F be the normal force acting on a surface of area A in contact with liquid, then hydraulic pressure exerted by the liquid on this surface is P = F /A. Hydraulic pressure is a scalar quantity because at one level inside the liquid, the pressure is exerted equally in all directions, which shows that a definite direction is not associated with hydraulic pressure. Please express your views of this topic Torque Problems by commenting on blog.

Derivation for Hydraulic Pressure Equation

Consider a liquid of density d contained in a cylindrical vessel of cross sectional area A. let h be the height of liquid column, and g be the value of acceleration due to gravity. The weight of liquid will exert a downward thrust on the bottom surface of the vessel. Therefore, pressure due to liquid acts on that surface. Is this topic capacitor electrolytic hard for you? Watch out for my coming posts.

Weight of liquid inside the vessel = volume × density of liquid × acceleration due to gravity

= Ah × d × g

Thrust of liquid on area A = weight of liquid = Ahdg

Hydraulic pressure on the base of vessel = P = Thrust / Area = Ahdg / A = h d g

Hydraulic Pressure = Height of the liquid column × density of liquid × acceleration due to gravity

Example for Hydraulic Pressure Equation

A 60 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of 1.5 cm. Find the pressure exerted by the heel on the horizontal floor?

Solution

Here, m = 60 kg, r = D / 2 = 1.5 / 2 = 3 / 4 cm = 3/400 m

According to the formula, Pressure = thrust / area

P = mg / `pi` r2

P = 60 × 9.8 / (22 /7) × (3/400)2 = 2.49 × 104 Pa.