CThe heat-transfer form of the energy equation: H₁ + Q = H₂
DBernoulli's equation is sufficient — shaft work does not affect incompressible flow
Bernoulli's equation applies only when there is no energy addition or removal — no pumps, turbines, or heat transfer. When a pump adds shaft work, you must use the extended form that includes the pump head h_pump as an addition on the inlet side. Option D is wrong: pumps absolutely affect incompressible flow, and ignoring shaft work gives incorrect results. Option C handles heat transfer, which is not the relevant term here (Q = 0). The extended Bernoulli is the correct tool for pump or turbine problems with incompressible flow.
Question 2 Multiple Choice
A steam turbine receives high-pressure steam at station 1 and exhausts lower-pressure steam at station 2. It produces shaft work W_s > 0. There is no heat transfer. Which energy balance is correct?
AH₁ = H₂ — enthalpy is conserved in steady flow through any device
BH₁ − W_s = H₂ — inlet enthalpy minus shaft work extracted equals outlet enthalpy
CH₁ + W_s = H₂ — shaft work adds to the fluid's energy at the outlet
DH₁ = H₂ + Q — a heat rejection term explains the enthalpy drop
The steady-flow energy equation is H₁ + Q − W_s = H₂. For a turbine with Q = 0 and positive shaft output W_s > 0, this gives H₁ − W_s = H₂. Outlet enthalpy is lower because the fluid has done work on the turbine shaft, transferring energy out. Option A (H₁ = H₂) would mean zero shaft work — contradicting the turbine operation. Option C has the sign wrong: shaft work out reduces the fluid's energy, not increases it. A quick check: energy must decrease when a turbine is present.
Question 3 True / False
Bernoulli's equation is a special case of the steady-flow energy equation that applies when shaft work and heat transfer are both zero.
TTrue
FFalse
Answer: True
This is precisely the relationship between the two equations. The steady-flow energy equation H₁ + Q − W_s = H₂ reduces to Bernoulli's equation when Q = 0 (no heat transfer) and W_s = 0 (no shaft work), and for incompressible flow where enthalpy differences reduce to pressure, velocity, and elevation terms. Bernoulli is not a separate law — it is the mechanical-energy-only special case of the general energy balance. Recognizing this hierarchy helps you choose which equation to apply.
Question 4 True / False
For a pump in a piping system, the steady-flow energy equation guarantees that fluid pressure is expected to increase between inlet and outlet.
TTrue
FFalse
Answer: False
A pump adds total head — the sum of pressure head, velocity head, and elevation head — not necessarily pressure alone. If the pump lifts water to a significantly higher elevation, much of the added energy goes into potential energy, and outlet pressure could actually be lower than inlet pressure. The energy equation correctly accounts for all energy forms. You cannot infer that pressure alone must increase just because a pump is present; you must account for all terms on both sides of the equation.
Question 5 Short Answer
What does the steady-flow energy equation add that Bernoulli's equation lacks, and why does this matter for analyzing real engineering systems like pumps and turbines?
Think about your answer, then reveal below.
Model answer: The steady-flow energy equation adds terms for shaft work (energy added by pumps or extracted by turbines) and heat transfer across the control volume boundary. Bernoulli only accounts for mechanical energy of the flowing fluid. Real systems almost always involve one or both of these interactions — a pump adds energy, a turbine extracts it, a heat exchanger transfers thermal energy. Without the shaft work term, you cannot compute how much pressure a pump adds or how much power a turbine produces.
In practice, the skill is recognizing which terms are zero for a given system and reducing to the appropriate simplified form. No heat transfer and no rotating machinery → Bernoulli. Pump present, incompressible, no heat → extended Bernoulli with pump head. Compressible fluid (steam) and turbine → full enthalpy formulation. Mastering the energy equation means learning to strip away irrelevant terms while keeping every term that matters for the specific device being analyzed.