MEC-28

Rankine cycle snapshot

η = (wt − wp)/qin with wt = h3−h4, wp = h2−h1, qin = h3−h2.

Reading speed

Heat enginesRankine

Governing equation

\eta=\dfrac{(h_3-h_4)-(h_2-h_1)}{h_3-h_2}

$h_3 \in \left[2500, 4000\right]$

where

h_1: Condenser liquid (kJ/kg)
h_2: After pump (kJ/kg)
h_3: Throttle inlet (kJ/kg)
h_4: Exhaust (kJ/kg)
\eta: Rankine efficiency (—)
w_t: Turbine work (kJ/kg)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\eta=\dfrac{(h_3-h_4)-(h_2-h_1)}{h_3-h_2}

$h_3 \in \left[2500, 4000\right]$

$h_3 = 2500$ $\eta = 0.085$

Along the curve

②

Domain of the variable — blue

h_3_{\min} = 2500,\quad h_3_{\max} = 4000

$h_3 \in \left[2500, 4000\right]$

$h_3 = 2500$ $h_3 = 2500$

Along the curve

③

Response curve — green

\eta=\dfrac{(h_3-h_4)-(h_2-h_1)}{h_3-h_2}

$h_3 \in \left[2500, 4000\right]$

$h_3 = 2500$ $\eta = 0.085$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\eta}{\mathrm{d}h_3}

$h_3 \in \left[2500, 4000\right]$

$h_3 = 2509.4$ $\eta^{\prime} = 3.94\times 10^{-4}$

Along the curve

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-28 — Rankine cycle snapshot) is the form associated with Rankine. Working symbols: $h_1$ , $h_2$ , $h_3$ , $h_4$ $\rightarrow$ $\eta$ , $w_t$ . The vapour power cycle: pump, boiler, turbine, condenser. Ideal Rankine ignores pressure drop.

Purpose

Purpose: compute

\eta

w_t

from

h_1

h_2

h_3

h_4

in Mechanical via

\eta=\dfrac{(h_3-h_4)-(h_2-h_1)}{h_3-h_2}

η = (wt − wp)/qin with wt = h3−h4, wp = h2−h1, qin = h3−h2. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

h_1 = 190.000\,\mathrm{kJ/kg}

h_2 = 195.000\,\mathrm{kJ/kg}

h_3 = 3400.000\,\mathrm{kJ/kg}

h_4 = 2300.000\,\mathrm{kJ/kg}

, the governing relation

\eta=\dfrac{(h_3-h_4)-(h_2-h_1)}{h_3-h_2}

yields

\eta = 0.3417\,\mathrm{—}

w_t = 1100.0\,\mathrm{kJ/kg}

. A T–s rectangle with a vapour dome, four state ticks. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Condenser liquid h_1190 kJ/kgAfter pump h_2195 kJ/kgThrottle inlet h_33400 kJ/kgExhaust h_42300 kJ/kg

Outputs

Rankine efficiency \eta0.3417 —
Turbine work w_t1100.0 kJ/kg

Reading speed

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Narration of this film

A T–s rectangle with a vapour dome, four state ticks.

The vapour power cycle: pump, boiler, turbine, condenser. Ideal Rankine ignores pressure drop.

Reading speed

Watch on YouTube