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BRAE 312 Ch 8 - Pipe Flow

# BRAE 312 Ch 8 - Pipe Flow - Hydraulics Pipeline Flow Ch 8...

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1 Hydraulics Pipeline Flow BRAE/ITRC Cal Poly Ch 8 Terms compressible v. incompressible laminar v. turbulent velocity v. flow rate friction loss minor losses ITRC/BRAE Cal Poly friction loss v. minor losses streamlines v. seamstress

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2 Laminar v. Turbulent h f varies by V n R crit = 2000 f ITRC/BRAE Cal Poly Re = Reynolds number = DV/ ν (full pipe) Derived in Chapter 7 (see also froude number) Froude Number Fr = v/(gA/w 0.5 Fr = v/(gA/w) v = average velocity (m/s) g = acceleration of gravity (m/s 2 ) A = flow area (m 2 ITRC/BRAE Cal Poly A flow area (m ) w = top width of water surface (m) Fr = 1 is critical flow
3 Kinematic Viscosity 0.01 0.001 ITRC/BRAE Cal Poly Reynolds Number Laminar Flow - Fluid particles moving in parallel layers and not mixing Turbulent Flow - Fluid particles mixing ITRC/BRAE Cal Poly between layers. Streamlines diffuse.

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4 Laminar v. Turbulent h f varies by V n R crit = 2000 f R = reynolds number = DV ν ITRC/BRAE Cal Poly R = reynolds number = DV/ 80 deg F water, 2 in pipe, V crit = 2,000 x 9.3 x 10 -6 ft 2 /s/ (2 in /12 in/ft) = 0.112 fps Laminar v. Turbulent ITRC/BRAE Cal Poly R = reynolds number = DV/ ν Example 80 deg F water, 0.5 in pipe and 12 in pipe, V crit = ? Is laminar flow important to drip irrigators?
5 Hydraulic Radius For non-circular pipes, another factor called the hydraulic radius is used in place of the diameter. By definition, the hydraulic radius is defined as being the cross-sectional area of flow divided by the wetted perimeter - ITRC/BRAE Cal Poly where fluid contacts boundary . R h = A/P Hydraulic Radius Pipe R h = A/P = π r 2 /2 π r = r/2 = D/4 ITRC/BRAE Cal Poly Rectangular Channel R h = A/P = b x y/ (b + 2y)

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6 Hydraulic Radius Solving Reynold's number problems for Solving Reynold s number problems for channels, substitute D = 4R h Open Channel Calculation Find V crit in rectangular channel 3 ft wide and 1.5 feet deep (80 deg water
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BRAE 312 Ch 8 - Pipe Flow - Hydraulics Pipeline Flow Ch 8...

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