Fluid Mechanics

Card # 18 Fluid Mechanics: Fluids are the substances which can flow like liquids and gases. Fluids lack definite shape and volume that is why it is convenient to use the quantities pressure and density rather than force and mass, while studying fluid statics and dynamics. Pressure in Liquid Suppose we have a cylindrical container of cross sect area A and height h, it is containing a liquid of density ρ . Then due to the weight (mg) of the liquid a normal force F acts on the bottom of the cylinder. Pressure at the bottom of the cylinder P = F/A = Force/Area of bottom Mass = Volume x density = m = Ah ρ P=Aρhg/A =ρgh Fluid Pressure A liquid or a gas is composed of molecules which are in a state of continuous random motion. When these molecules strike the surface of the container they impart moment to the surface. The momentum transferred per second to the surface gives the average force on the surface. This average force per unit area is the fluid pressure. Fluids in equilibrium For a fluid at rest the force due to fluid pressure always acts perpendicular to any surface which is in contact Fig: Liquid at rest in the container, a force F is acting on it which is making an angle θ with the free surface of the liquid Liquid at rest F cos θ = 0 or cos θ=0 or θ=90 Thus F is perpendicular to the free surface. At any point in a fluid at rest the pressure is the same in all directions. Pascal’s Law If we ignore gravity in a closed liquid at equilibrium the pressure applied at any point is equally transmitted in all directions and in the same amount. It means external pressure exerted on a static fluid is transmitted uniformly throughout the volume of the fluid. Hydraulic lift Hydraulic lift is an application of the Pascal’s Law. The principle of hydraulic lift is that by applying lesser force on small area we can get large force on large area. The principle of hydraulic lift cannot used in gases because gases are compressible and most of the efforts would go into compressing the gas rather than in to moving the load. Absolute and Gauge Pressure The total pressure at point A at a depth h = Absolute pressure P The free surface of a liquid experiences atmospheric pressure Pa which acts in downward direction. But pressure P at a point inside the liquid, according to Pascal’s principle, is the experience liquid pressure and additional atmospheric pressure. Pa = atmospheric pressure Gauge Pressure

Pg = hρ g

Pg = P − Pa