D5 · HVAC and Refrigeration Distribution and Systems

Foundation lesson · 18 minute study session

Convert the load before sizing the fuel path.

Move from useful heat to fuel input, then distinguish standard gas volume from meter volume.

By the end of this lesson

Translate an output duty into a fuel input on a stated efficiency basis.
Convert gas volume between stated absolute pressure and temperature conditions.
Identify the extra data needed for gas-pipe or fuel-oil selection.

Start with input and output.

An appliance output rating describes useful heat. Its fuel input must be larger when efficiency is below one. Use heating value and efficiency on the same HHV or LHV basis. A gas volume per hour is meaningful only with its reference temperature and pressure.

The meter has a state.

For the stated ideal-gas approximation, the same gas amount occupies a volume proportional to absolute temperature and inversely proportional to absolute pressure. Standard flow is not automatically actual pipe flow. At higher pressures, a supplied compressibility correction may be needed.

Capacity is more than nominal diameter.

After finding flow, choose a pipe method consistent with length, allowable pressure drop, gas properties and the stated code/table basis. Fuel oil requires its own density, viscosity and pump data. Do not put a liquid through a gas sizing equation or infer an installation rule from this energy balance.

A decision map for this lesson

One energy balance, two flow reference states

Calculate the fuel energy demand before converting the gas or oil flow to its required sizing basis.

Choose the governing relationship and catch the wrong route
Condition or question	Governing decision	Error to avoid
Useful appliance output is given	Find input with $\dot Q_{in}=\dot Q_{out}/\eta$ on the stated HHV or LHV basis.	Multiplying useful output by efficiency to obtain required input.
Gas heating value is per standard volume	Calculate standard flow, then convert actual meter volume with absolute pressure and temperature.	Using gauge pressure in an ideal-gas state conversion.
A gas sizing table is used	Match the flow reference, effective path length, allowed drop and property basis.	Omitting fitting length or entering actual cfm into a standard-flow table.
A fuel-oil circuit is sized	Use oil density and viscosity at the stated operating or startup condition.	Applying a gas-flow model or warm viscosity to a specified cold-start case.

On a narrow screen, scroll across the table to compare the decision and the error.

Relationships and their limits

Fuel input and standard flow

\dot Q_{in}=\dot Q_{out}/\eta;\qquad \dot V_s=\dot Q_{in}/H_s

Heating value $H_{s}$ must be energy per standard volume on the same basis as efficiency.

Actual-volume conversion

\dot V_a=\dot V_s\frac{P_s}{P_a}\frac{T_a}{T_s}

Ideal gas, same gas amount, absolute pressures and temperatures. Include compressibility when specified.

Symbols and unit basis
Symbol	Meaning	Units or basis
$\dot Q_{out}$	Useful appliance heat output	Btu/h
$\eta$	Thermal efficiency on stated basis	dimensionless
$H_s$	Heating value at standard conditions	Btu/standard ft³
$P$	Absolute gas pressure	psia
$T$	Absolute gas temperature	°R
$\dot V$	Volumetric flow	ft³/h at stated conditions
$\dot Q_{in}$	Fuel heat input	Btu/h

One decision, fully worked

Apply the method.

An appliance delivers 360,000 Btu/h at 80% HHV efficiency. Gas HHV is 1,000 Btu per standard ft³. Standard conditions are 14.735 psia and 520°R; the meter operates at 16.0 psia and 540°R. Assume ideal-gas behavior.

Find input heat before converting to gas flow.
Find standard flow using the supplied HHV.
Convert to meter volume using absolute conditions.

\dot Q_{in}=360{,}000/0.80=450{,}000\ \mathrm{Btu/h}

\dot V_s=450{,}000/1000=450\ \mathrm{standard\ ft^3/h}

\dot V_a=450\left(\frac{14.735}{16}\right)\left(\frac{540}{520}\right)=430.4\ \mathrm{ft^3/h}

Decision

The load requires 450 standard ft³/h, corresponding to about 430.4 actual ft³/h at the meter. Use the flow basis specified by the chosen sizing method.

Independent check

The pressure increase compresses the gas more than the temperature increase expands it, so actual volume is smaller than standard volume.

Specialist extension

Convert fuel energy and volume on the stated reference basis

A heating-value balance first establishes fuel energy input. For gas, match the heating value to the stated standard volume and keep actual pipe volume separate. Under an explicitly supplied ideal-gas relation, convert between actual and standard volumes with absolute pressure and temperature. Gas pressure loss still needs its applicable network model. For oil, use supplied density to convert volume and mass rather than a gas standard-volume correction.

A new applied case

Three simultaneous appliances deliver 200,000, 300,000 and 400,000 Btu/h useful heat. Each has 0.80 HHV efficiency. Gas HHV is 1,000 Btu/standard ft³. Actual absolute pressure is 1.25 times standard and actual absolute temperature is 1.10 times standard.

\dot V_s=(200{,}000+300{,}000+400{,}000)/(0.80\times1000)=1125\ \mathrm{standard\ ft^3/h}

\dot V_a=1125(1.10/1.25)=990\ \mathrm{actual\ ft^3/h}

Decision. The main must supply 1,125 standard ft³/h, equivalent to 990 actual ft³/h under the supplied ideal-gas conditions.

Cross-check. Higher actual absolute pressure reduces actual volume for the same amount of gas; the higher temperature partly offsets that reduction.

Unit basis. Heat rates are Btu/h on an HHV basis; efficiency is dimensionless; standard and actual volume rates are ft³/h at their respective conditions; pressure and temperature ratios are absolute.

NCEES PE Mechanical Reference Handbook v2.1; see the module reference path.

Open targeted practice in the study studio →

Transfer the method

HVAC and Refrigeration Distribution and Systems · HV-LC-D5

Try a new decision.

Select one

An appliance supplies 400,000 Btu/h at 80% HHV efficiency. Gas HHV is 1,000 Btu per standard ft³. Under an ideal-gas model, meter absolute pressure equals the standard absolute pressure, and meter absolute temperature is 1.10 times standard absolute temperature. The required actual meter-volume flow is most nearly:

A500 ft³/hB550 ft³/hC455 ft³/hD400 ft³/h

A lesson check supports practice, not a readiness score. Your response stays in this page session and clears on reload.

Catch the common errors

Dividing useful output directly by heating value without accounting for efficiency.
Using gauge pressure or Fahrenheit in a gas-law ratio.
Treating this flow calculation as proof that a pipe diameter meets a code.

Handbook navigation drill

Find it, then explain it.

Search: Heating value; meter pressure

Find the combustion section and the gas-meter heat-input relationship. Identify which temperature and pressure quantities are absolute.

Check your navigation

The handbook meter relationship corrects volume to its standard conditions. Read those reference conditions rather than assuming another industry convention.

Reference path: §3.3–3.6; §4.1–4.3; §10. These are printed handbook page numbers; section names and search terms remain the primary navigation method. See technical review status.

Theory sources

NCEES PE Mechanical Reference Handbook v2.1: §3.3–3.6; §4.1–4.3; §10
Mechanical and Electrical Equipment for Buildings, 12th ed.: mechanical systems and energy principles. Supporting theory; not an examination reference.

Worked examples and lesson prose are original ReasonSpan^™ material. Obtain authorized publications separately; this preview does not reproduce the supplied books or handbook.