MATHEMATICS: Ratio, Proportion, Variation - Power, Resistance of Conductor, Volume, Turbine Flowrate

1. POWER is directly proportional to DISPLACEMENT (total volume swept out by the pistons)


example:

A Honda engine delivers 240 horsepower and has a displacement of 3 liters. If displacement is changed to 3.8 liters, how much horsepower does the Honda engine deliver?


given:

P1 = 240 horsepower

D1 = 3 liters

D2 = 3.8 liters


find:

P2 = horsepower corresponding to a displacement of 3.8 liters


solution:


P = kD

k = P/D

k = P1/D1 = P2/D2

P1/D1 = P2/D2

240/3 = P2/3.8

P2 = 240 * 3.8/3

P2 = 304 horsepower



2. RESISTANCE OF CONDUCTOR is directly proportional to LENGTH OF CONDUCTOR


example:

If the resistance of 3 miles of transmission line is 170 ohms, what is the resistance of a 30-mile transmission line?


given:

R1 = 170 ohms

L1 = 3 miles

L2 = 30 miles


find:

R2 = resistance of a 30-mile transmission line


solution:



R
 = kL


k = R/L

k = R1/L1 = R2/L2

R1/L1 = R2/L2

170/3 = R2/30

R2 = 170 * 30/3

R2 = 1700 ohms




3. POWER is directly proportional to the FLOWRATE THROUGH THE TURBINES


example:

A turbine flowrate of 6000 gpm produces 45 MW. If the flowrate through the turbines is reduced to 3000 gpm (half), how much power would be produced?


given:

Q1 = 6000 gpm (gallons per minute)

P1 = 45 MW

Q2 = 3000 gpm


find:

P2 = power produced with 3000 gpm (half the flowrate through the turbines)


solution:


P = kQ

k = P/Q

k = P1/Q1 = P2/Q2

P1/Q1 = P2/Q2

45/6000 = P2/3000

P2 = 45 * 3000/6000

P2 = 22.5 MW --------> also half of the POWER would be produced, thus confirming a direct proportion