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13.2 Physics 6B Fluids - Hydrodynamics

13.2 Physics 6B Fluids - Hydrodynamics - Fluids...

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Fluids - Hydrodynamics Physics 6B Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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With the following assumptions, we can find a few simple formulas to describe flowing fluids: Incompressible – the fluid does not change density due to the pressure exerted on it. No Viscosity - this means there is no internal friction in the fluid. Laminar Flow – the fluid flows smoothly, with no turbulence. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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With the following assumptions, we can find a few simple formulas to describe flowing fluids: Incompressible – the fluid does not change density due to the pressure exerted on it. No Viscosity - this means there is no internal friction in the fluid. Laminar Flow – the fluid flows smoothly, with no turbulence. With these assumptions, we get the following equations: Continuity – this is conservation of mass for a flowing fluid. 2 2 1 1 v A v A t V = = Bernoulli’s Equation - this is conservation of energy per unit volume for a flowing fluid. 2 2 2 1 2 2 2 1 2 1 1 1 v gy p v gy p ρ + ρ + = ρ + ρ + Here A=area of the cross-section of the fluid’s container, and the small v is the speed of the fluid. Notice that there is a potential energy term and a kinetic energy term on each side. Some examples will help clarify how to use these equations: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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Example 1: Water travels through a 9.6cm diameter fire hose with a speed of 1.3m/s. At the end of the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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Example 1: Water travels through a 9.6cm diameter fire hose with a speed of 1.3m/s. At the end of the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We use continuity for this one. We have most of the information, but don’t forget we need the cross-sectional areas , so we need to compute them from the given diameters. 1 • 2 • 1 2 1 2 2 2 1 1 v A A v v A v A = = slower here faster here
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Example 1: Water travels through a 9.6cm diameter fire hose with a speed of 1.3m/s. At the end of the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the speed of the water coming out of the nozzle? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB We use continuity for this one. We have most of the information, but don’t forget we need the cross-sectional areas , so we need to compute them from the given diameters. 1 • 2 • 2 2 1 2 2 1 1 s m 1 m 00724 . 0 ) m 048 . 0 ( A 2 cm 6 . 9 r A 3 . 1 v = π = π = π = = 1 2 1 2 2 2 1 1 v A A v v A v A = = 2 2 2 2 2 2 2 2 m 00049 . 0 ) m 0125 . 0 ( A 2 cm 5 . 2 r A ? v = π = π = π = = slower here faster here Note:
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