[工学]Chapter 5 Energy in stead flow.ppt

5.1 Energies of A Flowing Fluid 5.2 Equation for Steady Motion of an Ideal Fluid Along a Streamline Take an infinitesimal element tube in steady flow field as shown, and regard the segment ds of the tube as control volume. The segment ds becomes a truncated cone when its curvature is neglected. Because the ideal fluid is frictionless and steady, the momentum equation in the flow direction is Because the segment is infinitesimal, the higher order infinitesimals may be omitted. Hence Indication: The differential relations are established among pressure, velocity and position of particle along an arbitrary streamline. 5.2.2 Bernoulli’s Equation and for incompressible fluid, ρ=constant，then So, Bernoulli’s Equation Application conditions： Physical meaning： in which, pressure potential energy— ：The work is done when the pressure brings a unit mass fluid from a position of p pressure to the position of zero pressure. Geometrical meaning： 5.2.3 Application of Bernoulli’s Equation Example 8 In 1773, Pitot used a bent tube to measure the velocity of stream in a river. Solution For a stream passing through point A and Point B And because Explaining (1) Total pressure at point A (Stagnation Pressure --PA ) (2) Static Pressure—PB 1) The pressure PB can be measured with a manometer moving at the same velocity as the flow’s. 2) If the change of static pressure on the section of pipe is neglected, the height of liquid in the little hole perpendicular to the pipe can represents the static pressure as shown. (3) Pitot-static pressure tube The velocity of flow is usually measured by Pitot-static pressure tube in engineering. Example 9 Analyze the principle of Venturi tube as shown in the figure. in which, is caused by viscosity and turbulence of fluid. Usually, =0.98~0.99 Example 10 Determine h’max of the siphon