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Open CalculatorAll Mechanical: Thermal and Fluid Systems PE Equations (9)
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Compressor Power (Ideal Gas, Adiabatic)
Power required for a steady-flow compressor including isentropic efficiency.
intermediateHigh Frequency -
Steady Conduction Through Plane Wall
Steady one-dimensional conduction through a plane wall.
basicHigh Frequency -
Convection Heat Transfer
Convection heat transfer from a surface to a fluid.
basicHigh Frequency -
Pipe Head Loss (Darcy–Weisbach)
Major head loss due to friction in a straight pipe.
intermediateHigh Frequency -
Heat Exchanger LMTD
Log-mean temperature difference for a two-stream heat exchanger.
intermediateHigh Frequency -
Ideal Gas Law
Relates pressure, volume, temperature, and mass of an ideal gas.
basicHigh Frequency -
Isentropic Temperature–Pressure Relation
Exit temperature for an isentropic compression/expansion of an ideal gas.
intermediateHigh Frequency -
Pump Hydraulic Power
Hydraulic power required to raise pressure/head of an incompressible liquid.
intermediateHigh Frequency -
Reynolds Number (Internal Flow)
Dimensionless Reynolds number for flow in a circular pipe.
basicHigh Frequency
Frequently Asked Questions
How do I use Compressor Power (Ideal Gas, Adiabatic) on the PE exam?
Always verify T2s is calculated correctly using isentropic relations or property tables. For ideal gases, use T2s/T1 = (P2/P1)^((γ-1)/γ). Watch units carefully - cp in kJ/(kg·K) gives power in kW, while cp in Btu/(lbm·°F) gives power in Btu/s. Typical compressor efficiencies range from 70-90%.
How do I use Steady Conduction Through Plane Wall on the PE exam?
Most commonly appears in composite wall problems. Always check if multiple layers require series resistance calculation (R_total = Σ(L_i/k_i·A)). Watch for temperature unit consistency - mixing °C and °F is a common trap. Heat flow direction: hot to cold, so T₁ > T₂.
How do I use Convection Heat Transfer on the PE exam?
Newton's Law of Cooling is fundamental - you must know typical h values and when to apply each. Remember that h depends on fluid properties, flow conditions, and geometry. Often given in problems, but may need to be calculated from Nusselt number correlations. Temperature difference drives the heat transfer.
How do I use Pipe Head Loss (Darcy–Weisbach) on the PE exam?
Always distinguish between Darcy friction factor (f) and Fanning friction factor (f_F = f/4). Moody chart shows Darcy factor. For smooth pipes, f ≈ 0.016-0.020; rough pipes f ≈ 0.025-0.035. Remember this is MAJOR losses only - add minor losses separately.
How do I use Heat Exchanger LMTD on the PE exam?
LMTD is only valid for pure counterflow or pure co-current flow. For multi-pass shell-and-tube or cross-flow heat exchangers, you must multiply by a correction factor F. Always check that ΔT₁ and ΔT₂ are calculated consistently (same end of heat exchanger). If ΔT₁ ≈ ΔT₂, LMTD approaches that common value.