EXAMPLE OF USE OF THE BERNOULLI EQUATION
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.EXAMPLE OF USE OF THEBERNOULLI EQUATIONFree jetsFigure 1From the fact, we found that;z1 hz2 0andp1 p2 0v1 0andThus, the fluid leaves as a “free jets” with;v2 2 ghThis is introduced in 1643 by Torricelli (1608-1647)1
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.Nozzle(a)(b)Figure 2We can safely use the centerline velocity at point (2)as a reasonable “average velocity”, as shown inFigure 2(a).If the exit is not a smooth, well-contoured nozzle, butrather a flat plate as shown in Figure 2(b), thediameter of the jet, dj will be less that the diameter ofthe hole, dh.This phenomenon is called a vena contracta effect, isa result of the inability of the fluid to turn the sharp90-degree corner indicated by the dotted line in thefigure.2
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.Figure 3The vena contracta effect is a function of thegeometry of the outlet. It can be obtained byexperimental, and called as contraction coefficient,Cc.Cc withAjAhAj is area of the jetAh is area of the hole3
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.The pitot-static tubeFigure 4The specific gravity of the manometer fluid shown inFigure 4 is 1.07. Determine the volume flowrate, Q,if the flow is inviscid and incompressible and theflowing fluid is water.4
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.The orifice nozzle / The nozzle meterFigure 5Determine the flowrate through the submerged orificeshown in Figure 5 if the contraction coefficient isCc 0.635
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.The venturi meterFigure 6JP-4 fuel (SG 0.77) flows through the Venturi metershown in Figure 6. Determine the elevation, h, of thefuel in the open tube connected to the throat of theVenturi meter.6
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.A rectangular weirFigure 7The volume flowrate, Q, follows that;Q C1 Hb 2 gH C1b(H )32(2g)7
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.A triangular weirFigure 8The volume flowrate, Q, follows that;Q C(12 2tan θ )(H )52(2g)8
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.The energy line and the hydraulic grade lineAs discussed before, the Bernoulli equation isactually an energy equation representing thepartitioning of energy for an inviscid, incompressible,steady flow.The sum of the various energies of the fluid remainsconstant as the fluid flows from one section toanother.A useful interpretation of the Bernoulli equation canbe obtained through the use of the concepts of thehydraulic grade line (HGL) and the energy line (EL).This ideas represent a geometrical interpretation of aflow and can often be effectively used to better graspthe fundamental processes involved.9
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.The energy line is a line that represents the total headavailable to the fluid. The elevation of the energy linecan be obtained by measuring the stagnation pressurewith a pitot tube.The static pressure tap connected to the piezometertube measures the sum of the pressure head andelevation head, and called piezometer head.The locus provided by a series of piezometer taps istermed the hydraulic line.Figure 910
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation.Figure 1011
Chapter 5 – Fluid in Motion – Examples of use of the Bernoulli equation. The energy line is a line that represents the total head available to the fluid. The elevation of the energy line can be obtained by measuring the stagnation pressure with a pitot tube. The static pressure tap connected to the piezometer
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Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. Crawford M., Marsh D. The driving force : food in human evolution and the future.
Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. 3 Crawford M., Marsh D. The driving force : food in human evolution and the future.
