Fluid Statics

Fluid Statics

• Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in motion.
• Any force developed is only due to normal stresses i.e, pressure. Such a condition is termed the hydrostatic condition.
• Fluid Statics is also known as Hydrostatics.
• A static fluid can have no shearing force acting on it, and that any force between the fluid and the boundary must be acting at right angles to the boundary.
• For an element of fluid at rest, the element will be in equilibrium. The sum of the components of forces in any direction will be zero. The sum of the moments of forces on the element about any point must also be zero.
• Within a fluid, the pressure is same at all the points in all the directions.
• Pressure at the wall of any vessel is perpendicular to the wall
• Pressure due to depth is P = ρgh, and is the same at any horizontal level of connected fluid.

Fluid Pressure at a Point: It a fluid is Stationary, then force acting on any surface or area is perpendicular to that surface.

If force is uniformly distributed over surface, then 

Its unit is pascal or Newton's per square metre.

1Pa = 1N/m²

1bar = 100kPa = 10⁵

Pa = 10⁵N/m²

Pascal’s Law: It states that pressure or intensity of pressure at a point in a static fluid (fluid is in rest) is equal in all directions. If fluid is not in motion then according to Pascal’s law,

p_x = p_y = p_z

Where, p_x, p_y and p_z are the pressure at point x,y,z respectively.

Hydrostatic Law: It states that rate of increase of pressure in vertical direction is equal to weight density of fluid at that point. e.g., if fluid is in rest, then balancing the force acting on small element of fluid is

Now, integrating from z = 0 to z = h depth, then pressure at h depth from free surface is:

Where, h is known as pressure head.