Pressure in Fluid A fluid exerts pressure in all directions. At any point in a fluid at rest, the pressure is the same in all direction. The force due to the fluid pressure always acts perpendicular to any surface it is in contact with.

Hydrostatic pressure The pressure in a liquid is due to the weight of the column of the liquid above it. P=  gh where  is the density of the liquid, h is the depth.

Fluid Flow Fluid Element A fluid element is the smallest volume of a fluid which follows the flow. Each fluid element follows the overall drift of the fluid motion. Flowline A flowline is the path which an individual fluid element describes.

Laminar Flow (Streamline Flow) Each particle of the fluid follows a smooth path, and these paths do not cross over one another. Successive particles passing a given point have the same velocity. The flow is steady.

Turbulent Flow Turbulent flow is characterized by erratic, small, whirlpool-like circles called eddy currents. The velocity of particles at a given point depends on the instant of observation. Fluid elements passing a given point do not follow the same path.

Streamline (1) A streamline is a flowline in which every fluid element along the line follows the same path. The instantaneous velocity of a fluid particle at a point lies along the tangent to the streamline at that point. Streamlines can never cross.

Streamline (2) A given fluid element moving along a streamline may change its speed and direction as it moves along the streamline. At any fixed point on a stream, the velocity of the fluid is fixed. The density of the streamlines indicates the speed of the fluid. The crowded streamlines indicate that the speed of the fluid is high.

Continuity Consider steady flow along a pipe as shown below. A1A1 A2A2 The mass per second entering the pipe = the mass per second leaving v2tv2t v1tv1t

Equation of Continuity  vA = constant where  = fluid density v = fluid speed A = cross-sectional area of the pipe If the fluid is incompressible, then we get A 1 v 1 =A 2 v 2 The product Av represents the volume rate of flow.

Bernoulli ’ s Principle (1) To be general, consider the fluid flowing in a tube of non-uniform cross section that varies in height above some reference level. Assume that the flow is steady and laminar, the fluid is incompressible, The viscosity is small enough to be ignored.

Bernoulli ’ s Principle (2) Bernoulli ’ s equation For streamline motion of an incompressible non-viscous fluid, the sum of the pressure at any point plus the kinetic energy per unit volume plus the potential energy per unit volume there is always constant. For horizontal flow, the pressure is low where the velocity is high.

Perfume Atomizer (Paint sprayer) The larger force of the slow moving air in the container pushes down on the surface of the liquid while the faster moving fluid reduces the pressure on the open end of the tube.

Filter Pump The pressure inside the pump is reduced by the rapid stream of water. Because of the difference in pressure, air from the chamber is removed. Water stream To chamber to be evacuated Water and air

Carburettor The flowing air speeds up as it passes the constriction so the pressure is reduced. This draws the petrol vapor into the air stream. Air stream Air-petrol mixture Petrol Tank

Aerofoil lift The faster the wing goes, the more lift it produces. The thinner the airfoil is in height, the less lift it will create.

Sailing against the Wind Sails are arranged so that the air velocity increases in the narrow constriction between the two sails, creating a decrease in pressure.

Spinning Baseball The top of the ball is moving forward against the air and meeting resistance while the lower half is spinning backward and moving in the same direction as the air. The air pressure above the ball is greater than the pressure below, causing the ball to curve downward.

Spinning Golf Ball The dimples cause the flow to become turbulent at a lower velocity than on a smooth sphere. This in turn causes the flow to remain attached longer on a dimpled golf ball which implies a reduction in drag.

Venturi meter A venturi meter is usually use to measure the flow speed of fluid. The flow speed can be obtained by A1v1A1v1 A2v2A2v2

Fluid flow Pitot-Static Tube (1) Static pressure The static pressure (P S ) at a point is the pressure on a small surface parallel to the flow. Total pressure The total pressure (P T ) at a point is the pressure on a small surface at rest placed head-on to the flow. h Static tube Total tube

Pitot-Static Tube (2) At any given point, P T >P S. The difference between P T and P S depends on the fluid speed. The fluid at the tip of the total tube is at rest. That is, v T =0. The fluid flow is unaffected on passing the mouth of the static tube. That is, v S =v where v is the undisturbed flow speed. According to Bernoulli ’ s principle,

Pitot-Static Tube (3) The diagram shows a version of Pitot-static tube to measure speed of air.