chap0040

chap0040 - Flow Resistance: Laminar and Turbulent Flows In...

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Flow Resistance: Laminar and Turbulent Flows In Pipes & Channels By M.S. Ghidaoui, Spring 2002 I highly recommend you watch the video cassette entitled ``turbulence’’ which is available in the HKUST library. The call number is TA 357 F578 1990 V.26. Introduction: Laminar Flow Velocity Profile: velocity distribution (Laminar Flow) v t Velocity at a point in a steady laminar flow Turbulent Flow Velocity Profile: v instantaneous velocity distribution (Turbulent flow) v t Velocity at a point in a turbulent flow---varies with time although the flow boundary conditions are fixed! Time average velocity distribution
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The time averaging is performed over a time T long enough compared to the time scale of turbulence. Characteristics of Laminar Flow: 1. Poor mixing capability (only molecular diffusion). 2. Orderly motion. The fluid moves in layers (laminae). 3. Vorticity is regularly distributed in either 2 or 3 dimensions in space. 4. Near true steady conditions can be achieved. Poor mixing properties (only molecular). 5. Energy dissipation is proportional to viscosity and velocity gradient for Newtonian fluids (i.e., dy du μ τ = ). Laminar flows are usually characterized by relatively small energy dissipation (i.e., small head loss). y y du dy Shear stress distribution in a pipe. Examples of laminar flows: Often groundwater flows are laminar; blood flows etc. The study of turbulent flows is important for some civil engineering applications. Examples include: Groundwater modeling. Water quality modeling in groundwater. Infiltration and slope stability. Seepage in dams and foundation. Settling of particles in water treatment plants. Characteristics of Turbulent Flow: 1. Efficient mixing of mass, momentum and energy (turbulent diffusion is much higher than molecular diffusion). 2. Disordered motion. 3. Vorticity is irregularly and continuously distributed in 3 space dimensions. 4. Turbulent mixing generally results in high energy dissipation (i.e., large head losses). 5. Instantaneously, the flow is never steady and always 3 dimensional! However, if many velocity samples are collected at a point and averaged in time, the averaged velocity may approach steady condition.
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6. Turbulent flow is never reproducible in details. Only time-averaged quantities are reproducible. Examples of Turbulent Flows: pipe flows for water supply; open channel flows (natural and human made); winds and typhoons; ocean flows; flow inside a pump etc. The study of turbulent flows is important for many civil engineering applications. Examples include: water quality modeling; sediment transport; energy dissipation in pipes, sewers and natural open channels; fluid structure interaction (wind loading and structural vibration); Note: dy dv near the pipe wall for turbulent flow is much larger than dy dv for laminar the wall shear in turbulent flow is much larger than the wall shear in laminar flow.
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chap0040 - Flow Resistance: Laminar and Turbulent Flows In...

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