Bernoulli, continuity, pipe flow losses, pumps, conduction, convection, radiation, heat exchangers and dimensionless numbers.
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- State Bernoulli's equation for steady, incompressible flow
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P/ρg + v²/2g + z = constant, or P₁/ρg + v₁²/2g + z₁ = P₂/ρg + v₂²/2g + z₂- What are the main assumptions for Bernoulli's equation to be valid?
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Steady flow, incompressible fluid, frictionless (inviscid) flow, flow along a streamline- What does pressure head represent in Bernoulli's equation?
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The height of fluid column that pressure can support, or P/(ρg)- What does velocity head represent in Bernoulli's equation?
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The height equivalent of the kinetic energy per unit weight, or v²/2g- What does elevation head represent in Bernoulli's equation?
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The potential energy per unit weight of the fluid, or height z above a reference datum- Bernoulli's equation relates three forms of what?
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Mechanical energy: pressure energy, kinetic energy, and potential energy- State the continuity equation for incompressible flow
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A₁v₁ = A₂v₂, or volumetric flow rate Q is constant- In a converging pipe, how does velocity change as area decreases?
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Velocity increases (inverse relationship with area)- What is the relationship between mass flow rate and continuity?
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Mass flow rate is constant throughout: ṁ = ρAv = constant for steady flow- What physical principle does the continuity equation express?
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Conservation of mass in a flowing fluid- If a pipe area decreases by half, by what factor does velocity change?
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Velocity doubles (increases by a factor of 2)- What are major losses in pipe flow?
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Friction losses along the pipe wall due to viscous shear stress- State the Darcy-Weisbach equation for pipe friction losses
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hf = f(L/D)(v²/2g), where f is friction factor, L is pipe length, D is diameter- What does the friction factor f in Darcy-Weisbach represent?
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A dimensionless number accounting for pipe roughness and flow regime- Define Reynolds number and state its formula
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Re = ρvD/μ = vD/ν, the ratio of inertial to viscous forces
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