you are looking at buying a portable fire pump so that you can use
swimming pool water to fight bush fires at your house.you find the
pump(5hp engine,water pressure at pump 76psi, hose length 10m, hose
diameter 40, volume flow 250 litres/minute).what would be the water
pressure at the hose outlet and how long will it take to empty the
pool which is 25m by 12m and an average of 1.5 deep. you can get a 20m
long hose which would suit you better but the diameter hose is reduced
to 25mm. what sort of pressure would you get at the hose do you think
it would be enough.the poisseille equation you use for the above
calculations assume laminar flow. is that assumption valid. thanks

mango1952-ga,

From the following websites we get the Poiseulle equation for laminar
flow in a pipe :

http://landau1.phys.virginia.edu/classes/241L/poise/poise.htm
http://www-unix.oit.umass.edu/~phys131f/11_18.pdf (gives info about mu
for water)

    pi * Dp * r^4
F = ------------
     8 * mu * l

F  = volume of flow per unit time
pi = 3.14159...
Dp = change in pressure at either end of pipe
r  = radius of pipe
mu = coefficient of viscosity
l  = length of pipe

In general we assume that mu for water is 1 x 10^-3 = 0.001.

For the 10m pipe, we have :
l = 10m
r = 20mm = 0.02m

The pump has :
F = 250 l/min = 4.1667 l/sec = 0.004167 m³/sec

So using the poiseulle equation we get:

           3.14159 * Dp * 0.02^4
0.004167 = ---------------------
               8 * 0.001 * 10

So Dp = 0.004167 * 8 * 0.001 * 10 / (3.14159 * 0.02^4)
      = 663.146 g/m²
      = 663.146 / 6890 = 0.1 psi (approx)

So the pressure at the outlet will be 76 - 0.1 = 75.9psi

The volume of the pool is 25m x 12m x 1.5m = 450m³

At a rate of .25m³/min, it would take 450/.25 = 1800 minutes = 30
hours

to empty the pool.

For the 20m pipe, we have :
l = 20m
r = 12.5mm = 0.0125m

So Dp = 0.004167 * 8 * 0.001 * 20 / (3.14159 * 0.0125^4)
      = 8691 g/m²
      = 8691 / 6890 = 1.26 psi (approx)

The final pressure will still be 76 - 1.26 psi = 74.74 psi, which
still seems suitable.

A good example of the difference between laminar and turbulent flow is
given at the bottom of the following site :

http://www.uvi.edu/Physics/SCI3xxWeb/Plumbing/FluidDynamics.html

As you can see, laminar flow requires that all flow is parallel to the
sides of the pipe (the Poisseuile equation requires a horizontal pipe
- this may not be the case for fighting a fire). In general this
should be a good approximation - however you will not have laminar
flow :

1) at the connection to the pump
2) at curves or kinks in the hose
3) at the open end of the hose

The effect of these should be minimal.

I had to make a few assumptions to answer your question. The first was
to ignore the effect of getting the water from the bottom of the pool.
If this is the case, then you need to reduce the pressure by :

delta P = rho*g*deltaH = (approx) 9800 * 1.5 = 2.14 psi

Let me know if you have any further concerns and I will do my best to
address them.

Regards

calebu2-ga

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