Bernoulli ’ s Equation

Outline The Energy Balance for a Steady Incompressible Flow The Friction Heating Term Bernoulli ’ s Equation The Head Form Diffusers and Sudden Expansions Bernoulli ’ s Equation for Gases

Outline (Continued) Torricelli ’ s Equation Bernoulli ’ s Equation for Fluid Flow Measurement Pitot Tube Venturi Meter Orifice Meter Rotameter

Outline (Continued) Torricelli ’ s Equation Negative Absolute Pressures, Cavitation Unsteady Flows Non Uniform Flows

Objectives Introduce Bernoulli ’ s equation. Apply it to the case of diffusers and sudden expansions. Introduce devices to measure local velocity and flow rate. Introduce Torricelli ’ s equation. Explain cavitation.

Objectives (Continued) Study the validity of the equation in the case of gas flow. Study the validity of the equation in the case of unsteady-state flow problems. Apply the equation in the case of non- uniform flow.

Summary Basic assumptions: steady state and incompressible flow. Bernoulli ’ s equation: Head form:

Summary (Continued) For diffusers and sudden expansions, kinetic energy loss is converted to friction heating, and increase in pressure. Bernoulli ’ s equation is practically correct for low-velocity gas flows. Torricelli ’ s equation:

Summary (Continued) Local velocities can be measured by Pitot tube for open channel and flow in pipes. Venturi meter and orifice meter are flowrate measurement devices. Friction effects are accounted for by introducing empirical coefficients. The venturi meter causes little pressure loss but it is expensive. It is used for large volumetric flow rates. The orifice meter is used for small volumetric flow rates.

Summary (Continued) Rotameters require calibration. Absolute pressures are unrealistic. They mean: velocities are too high in the case of gases and they mean the presence of cavitation in the case of liquids.

Summary (Continued) In the case of unsteady flows, Bernoulli ’ s equation can be applied if or if acceleration is due to pressure.

Summary (Continued) In some cases, it is important to account for non-uniformity of the flow while using Bernoulli ’ s equation (example: flow over a weir).