The Physics of
Fireground Hydraulics
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Formulas
By simplifying the physics down to an equation with few terms, mental
math on the fire scene is less stressful. Fire Apparatus
driver/operators can deduce the correct pressure to set their pump at
using 2 equations.
First, the formula for Friction loss (FL) due to water traveling
through a length of hose is given by
FL=CQ^2L and values are calculated by
FL=C(Q/100)^2(L/100) (1
where C=coefficient for hose of a given diameter
Q=quantity of water flowing, in gallons per minute
L=lenth of hose in feet
Second, Engine Pressue (EP) is the sum of friction loss through hose
and appliances, nozzle pressure, and elevation.
EP=NP+FL+Elev (2
Where nozzle pressure is the pressure required at the tip of an
appliance to discharge a predetermined flow rate
and elevation is accounted for by adding 5psi for every 10 feet of
vertical gain, -5psi per 10ft drop.
Ex)
Find the engine pressure for Engine 11, flowing a 300' 3" skid load at
standard pressure. Using values from
Cheat
Sheet, we know the
initial pressure a.k.a. Nozzle Pressure is 145psi and the coefficient
for 3" hose is 1. First we find friction loss of the water
flowing through 300' of 3" at 300gpm (two 150gpm attack lines branch
from the 3" line). FL=(1)(300/100)^2(300/100)=9(3)=27psi.
Now we plug our NP and FL into
equation 2, which gives EP=145+27+0(elevation)=172psi.
This means that E11 must pump at 172psi to provide 300gpm to its
300' skid load.