Fluid mechanics is the branch of physics related to flowing fluids. The motion of a liquid can take quite complicated forms. For the simple case of an incompressible liquid, flowing in a non-turbulent way, we have two very useful equations. The liquid flows faster when the area becomes smaller. The product of speed and cross sectional area of the flow is constant along the pipe. Thus A 1 * v 1 = A 2 * v 2 The equality above is called the equation of continuity. The equation of continuity is a direct result of the conservation of mass. The dimensions of the product, (area)*(velocity), is the volume of liquid flowing past a point in unit time: [m 2 * m/s] = [m 3 /s] [volume/time]. The equation of continuity holds for all incompressible fluids.
Bernoulli’s Equation The pressure-depth relationship, P=pgh, holds only for stationary liquids. A liquid can have different pressure at two points of the same depth, if it is flowing at different speeds at these points. The pressure of a fluid decreases with increasing speed. If the height of the liquid is also changing over the length, the potential energy change must be included in the derivation. The result given below is known as Bernoulli’s equation: P 1 + ½pgh 1 = P 2 + ½pv 22 + pgh 2
Ex: 1. Water flows through a pipe of varying cylindrical cross-section. The speed of the water is 4 m/s when the pipe radius is 3 m. What is the speed of water through a cross-section of 6 m radius? (2 zada 4 u poka ne piwite, skoro ispravim I zakinem snova) 2. Water comes out of a tap at a speed of 1 m/s. The cross-sectional area of the water exit is 2 cm 2. How many kilograms of water is wasted when the tap is accidentally left on for 1 hour?
Скачать презентацию Fluid mechanics is the branch of physics related
fluid_mechanics.pptx