Pressure, flow, pipes and pumps. Continuity and Bernoulli carry most of the load.
Choose any section below to get a free practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
Pressure in a still fluid grows with depth: p = ρgh, or γh with specific weight γ = ρg.
A mercury manometer (SG 13.6) shows a 0.2 m difference between two air-filled lines. What is the pressure difference?
Δp = 13.6(9810)(0.2) = 26.7 kPa.
Common trap: (B) uses water instead of mercury.
Fluid MechanicsHydrostatic PressureManometersBuoyancyThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Mass is conserved, so for an incompressible fluid Q = A1v1 = A2v2.
Water speeds up from 2 m/s to 8 m/s in a horizontal reducer. What is the pressure drop, neglecting losses?
p1 − p2 = ½ρ(v22 − v12) = ½(1000)(64 − 4) = 30 kPa.
Common trap: (A) forgets the ½.
Continuity EquationBernoulliPitotThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
The Reynolds number Re = VD/ν tells you the flow regime: laminar below about 2,300, turbulent above about 4,000.
Water (ν = 1 × 10−6 m2/s) flows at 0.04 m/s in a 50 mm pipe. What is the Darcy friction factor?
Re = (0.04)(0.05)/10−6 = 2,000, laminar. f = 64/Re = 0.032.
Common trap: (D) is 64/1000; recheck Re.
Reynolds NumberDarcyMoodyminor lossesThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
A pump adds head H; the power it needs is ρgQH/η.
A water jet (Q = 0.01 m3/s, v = 20 m/s) hits a flat plate head-on and spreads sideways. What force does it exert?
F = ρQv = 1000(0.01)(20) = 200 N.
Common trap: (B) assumes the jet reverses direction.
PumpsAffinity LawsImpulse-MomentumDragThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Venturi, orifice and nozzle meters convert a pressure drop into flow: Q = CdA√(2Δp/ρ) (for a small throat-to-pipe area ratio).
An orifice meter (Cd = 0.62, 50 mm orifice) shows a 20 kPa drop in water. Estimate the flow.
A = 0.001963 m2. Q = 0.62(0.001963)√(2 × 20,000/1000) = 0.62(0.001963)(6.32) = 0.0077 m3/s.
Common trap: (B) leaves out Cd.
Flow MeasurementorificeSimilitudeMachThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Gas flow becomes compressible above about Mach 0.3, where Ma = V/c and the speed of sound in an ideal gas is c = √(kRT), with T absolute and R in J/kg·K (287 for air).
What is the speed of sound in air at 70 °F? Use k = 1.4, R = 53.35 ft·lbf/lbm·°R and gc = 32.174 lbm·ft/lbf·s2.
T = 70 + 460 = 530 °R. c = √(kgcRT) = √(1.4 × 32.174 × 53.35 × 530) = 1,130 ft/s.
Common trap: (A) leaves out gc, so the units never reduce to ft/s.
Mach NumberIsentropic Flow RelationshipsNormal Shock RelationshipsCompressible FlowThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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