When a liquid is contained in a vessel, it exerts force at all points on the sides and bottom of the vessel. The force per unit area is called intensity of pressure. Mathematically, intensity of pressure,
p = P/A
where
P = Force acting on the liquid, and
A = Area on which the force acts.

The intensity of pressure at any point, in a liquid at rest is equal to the product of weight density of the liquid (w) and the vertical height from the free surface of the liquid (h). Mathematically, intensity of pressure,
p = w. h

From this expression, we see that the intensity of pressure at any point, in a liquid, is directly proportional to depth of liquid from the surface.

When a liquid is contained in a vessel, it exerts force at all points on the sides and bottom of the vessel. The force per unit area is called intensity of pressure. Mathematically, intensity of pressure,
p = P/A
where
P = Force acting on the liquid, and
A = Area on which the force acts.

The intensity of pressure may be expressed either in N/m², N/mm² or in metres of liquid or mm of liquid. Intensity of pressure is also expressed in pascal (briefly written as Pa), such that
1 Pa= 1 N/m²; 1 kPa= 1 kN/m² and 1 MPa = 1 MN/m²= 1 N/mm²

According to Pascal’s law, the intensity of pressure at any point in a fluid at rest is same in all directions.

The important dimensionless numbers in fluid mechanics are
1. Reynold’s number
2. Froude’s number
3. Weber’s number
4. Euler’s number
5. Mach’s number or Cauchy’s number

Reynold’s number: Reynold’s number is the ratio of inertia force to the viscous force.

Froude’s number: Froude’s number is the ratio of inertia force to the gravity force.

Weber’s number: Weber’s number is the ratio of inertia force to the surface tension force.

Euler’s number: Euler’s number is the ratio of inertia force to the pressure force.

Mach’s number or Cauchy’s number: Mach’s number or Cauchy’s number is the ratio of inertia force to the elastic force.