The System
Darby’s name for the region of space you choose so you can write mass, energy, and momentum balances on it.
What is the system?
In - out = accumulation.
At steady state this is zero.
What is the (macroscopic) mass balance?
First-law statement that energy is neither created nor destroyed, only transferred or stored.
What is conservation of energy?
Mechanical energy turned into internal energy by viscosity, fittings, and turbulence. It cannot be turned fully back into work.
What is friction loss? / What is ef?
Newton's second law written for a flowing system: ∑F = mVout - mVin (steady, one stream).
What is conservation of momentum?
The surface that separates "inside the system" from "the surroundings."
What is the system boundary?
The microscopic mass balance divided by dx dy dz dx. For incompressible flow it becomes ∇ ⋅ v = 0.
What is the continuity equation?
ΔP/ρ + gΔz + Δ(αV2/2) = 0
What is the Bernoulli equation?
Factor that corrects V2/2 because the velocity is not uniform across the pipe. About 2 in laminar flow, about 1 in turbulent flow.
What is the kinetic-energy correction factor α (alpha)?
Dimensionless number Kf = ef/(V2ref/2) used for valves, fittings, and sudden expansions.
What is the loss coefficient?
A system that mass does cross (pipe, pump, tank with a free surface).
What is an open system?
Tank quantity that does not change while you pump air out.
What is volume?
Sign of pump w in Darby’s when the pump does work on the fluid.
Fanning ef=2fLV2/D
What is pipe friction loss?
Torque form of Newton’s second law. Used for mixers, turbines, and rotating machinery.
What is conservation of angular momentum?
For the vacuum-tank problem, mass entering the system.
What is zero?
Steady tank, 200 gpm in, hole in the bottom. What is the outflow.
What is 200 gpm?
-w/g in feet of fluid.
What is pump head?
Two sources of ΔT in an insulated line with an inefficient pump.
What are friction and pump inefficiency?
A cable is best at carrying this type of load.
What is tension?
A system that mass does not cross (sealed tank, piston + gas).
What is a closed system?
dm/dt = ρAV = ρQ
What is mass flow rate?
Work the fluid does on a turbine, or work a pump does on the fluid, per unit mass.
What is shaft work w?
Pressure rises in an expanding air tube, but ef is still positive.
What is a drop in kinetic energy?
loop In the relief-valve problem, the velocity used to define Kf.
What is inlet velocity?