(42S) Pulley Sheave and Fan Laws

[Eddie W. Shore]

Basic Pulley Law - Fans

The basic relationship between a fan and it's motor is simple:

rpm1 * dai1 = rpm2 * dia2

where:

rpm1: how fast the fan turns, in revolutions per minute
dia1: the diameter of the fan's pulley
rpm2: the speed of the motor, in revolutions per minute
dia2: the diameter of the motor's pulley

A diagram is shown below of a motor-pulley/fan-pulley system. The actual length of the pulleys will vary per system.

The program PULLAW sets up the solver for this law. To call up the solver, press [(shift)] [ 7 ] (SOLVER), select PULLAW.

HP 42S/DM42/Free42 Solver Program: PULLAW

Code:


00 { 59-Byte Prgm }
01▸LBL "PULLAW"
02 MVAR "RPM1"
03 MVAR "DIA1"
04 MVAR "RPM2"
05 MVAR "DIA2"
06 RCL "RPM2"
07 RCL× "DIA2"
08 RCL "RPM1"
09 RCL× "DIA1"
10 -
11 END

Basic Sheave Law

The basic sheave law listed below describes how adjusting a sheave's airflow affects the motor's break horsepower:

bhp2 = (cfm2 / cfm1) ^ 3 * bhp1

CFM: cubic foot per minute (airflow)
BHP: brake horsepower of the motor

The program SHLAW sets up the solver for this law. To call up the solver, press [(shift)] [ 7 ] (SOLVER), select SHLAW.

HP 42S/DM42/Free42 Solver Program: SHLAW

Code:


00 { 60-Byte Prgm }
01▸LBL "SHLAW"
02 MVAR "BHP1"
03 MVAR "CFM1"
04 MVAR "BHP2"
05 MVAR "CFM2"
06 RCL "CFM2"
07 RCL÷ "CFM1"
08 3
09 Y↑X
10 RCL× "BHP1"
11 RCL- "BHP2"
12 END

Basic Fan Laws

Three basic ratios are used in dealing in fan engineering, which are:

cfm ratio = cfm2 / cfm1 = rpm2 / rpm1

sp ratio = sp2 / sp1 = (rpm2 / rpm1) ^ 2

hp ratio = hp2/ hp1 = (rpm2 / rpm1) ^ 3

where:

rpm: a fan's revolution per minute. rmp1 and rpm2 represents different conditions of the fan

cfm: airflow of a fan in cubic feet per minute. You can use other units, just be consistent.

sp: static pressure of a fan

hp: break horsepower of a fan

HP 42S/Free42/DM42 Program: FANLAW

Code:


00 { 74-Byte Prgm }
01▸LBL "FANLAW"
02 "RPM2?"
03 PROMPT
04 "RPM1?"
05 PROMPT
06 ÷
07 STO 01
08 CLA
09 "CPM RATIO ="
10 AVIEW
11 STOP
12 ENTER
13 ENTER
14 ENTER
15 ×
16 STO 02
17 CLA
18 "SP RATIO ="
19 AVIEW
20 STOP
21 ×
22 CLA
23 "HP RATIO ="
24 AVIEW
25 .END.

Source:

Gladstone, John Air Conditioning Testing and Balancing: A Field Practice Manual Van Nostrand Reinhold Company. New York. 1974 ISBN 0-442-22703-5