# lecture 17 - Thermal and Fluids Engineering I Lecture 17...

This preview shows pages 1–4. Sign up to view the full content.

Thermal and Fluids Engineering I Lecture 17 Page 1 Lecture 17 – Turbulent Flow Reynolds Number For fully-developed laminar flow in a horizontal pipe: 2 8 m L P R µ ∆= V The pressure drop, P , depends on , , ,and . m LR V In turbulent flow, P also depends on these four parameters, but the relationship is more complex. To reduce the number of variables, we non-dimensionalize. 2 2 83 2 2 mm LL P D D µµ = ⎛⎞ ⎜⎟ ⎝⎠ VV To find a representative pressure, consider Bernoulli’s equation along a streamline in stagnation flow: 22 11 2 2 12 PP gz gz ρρ ++ = 2 2 2 P P += V

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Thermal and Fluids Engineering I Lecture 17 Page 2 2 1 12 2 P P ρ += V static pressure + dynamic pressure = stagnation pressure We now use dynamic pressure to define a non-dimensional pressure as: * 2 1 2 m P P ∆= V Also define a non-dimensional length * L L D = () * *2 2 32 1 2 m m DL P D µ ⎛⎞ ⎜⎟ ⎝⎠ V V * * 64 m P LD = V Define the Reynolds number as char L Re = V where L char is a characteristic length for the geometry under consideration. In a tube flow, L char is D . * * 64 D P LR e = laminar, fully developed This is a non-dimensional pressure drop per unit length of pipe. It depends only on the Reynolds number. By experiment in pipe flow:
Thermal and Fluids Engineering I Lecture 17 Page 3 Re < 2100 laminar 2100 < Re < 4000 transitional 4000 < Re turbulent Friction Factor Define the Darcy friction factor as * * P f L = Since * 2 1 2 m P P ρ ∆= V and * L L D = 2 1 2 m P f L D = ⎛⎞ ⎜⎟ ⎝⎠ V 2 2 m L Pf D V laminar or turbulent

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

lecture 17 - Thermal and Fluids Engineering I Lecture 17...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online