As we try to understand
what is the right pump for our system we need to understand our system
hydraulics - and our system performance first we do that we create what is known
as the system
curve. To help develop this idea have this general, very big, schematic
of a pumping system where we have the reservoir at a
lower elevation pumping up to the reservoir at a higher elevation
in the middle is the pump. The main tool to use
is conservation energy. And in this case is just like
when you go to solve a energy between two known points
except we add in the term of
the, what they call the, pump head into the equation.
This equation can be simplified because the starting and ending points
are open-air reservoirs where
essentially, the velocity of the flow
is a rest, right? So we can cancel out the velocity 1, and
the velocity 2. Also if you take a second think about it -
both reservoirs are at the same pressure whatever is
they will also be cancelled out because they are equal.
So we can solve this equation for
what was often referred to as the pump head
by moving z1 over to the right hand side
and being left with these Terms. z2 minus z1 plus the friction head
loss plus
the minor head losses. We start inserting values into this
you know we have on this particular example
the Darcy-Weisbach friction factor given to us
so we'll use the Darcy-Weisbach equation
it
it provides us the opportunity to bring in Q into the equation - the flow rate.
We can also ignore the minor losses for now
because in a system that's fairly large the minor losses usually don't add up to
much over the
over the whole the system. So
knowing that we used Darcy-Weisbach we can actually put in the specific
values
that were given to us in the problem and calculate the pump head in terms of the
the elevation heard plus some factor times the Q -
time the flow rate. That gets us this equation,
where we can simplify it down to
Hp is equal to 30 feet -
that's the elevation had we need to overcome - plus
the friction head that we need to overcome. So if you are doing this all by
yourself, go ahead and take a moment and
stop right now, calculate that factor
and insert it into that space next to the Q squared.
Did you happen to get
15.8? I hope so. It'd be handy if you did then I know I did it right.
What this does for us is it gives us
a way to plot all
of the performance of the system as the discharge in the system
varies so on your handout you can
fill in the flow rates at 500, 1000
1500, 2000, 2500 and so forth so that you have the x axis values ready to go.
Darcy-Weisbach equation uses Q
in cubic feet per second so we take our gallons per minute
then insert in all the CFS
values. And now that we have the CFS values we can use our system curve
equation
to tell us what is the corresponding head that needs to be overcome in the
system.
With this information we can go ahead and start plotting that on our graph is
the skill I plan to use
just plot these points in. It's going to be a nice parabolic shape
related to the fact that we gotta Q squared term
and this sort-of gives you a bit of an overview
of how to create a system curve
the system curve equation - just as a quick review - comes from
the conservation of energy formula. We can cancel out the pressures and the
velocities
and then we just solve for the pump
head in terms of all the other terms so that we get down to a pump head
plus the elevation difference plus
some factor times Q squared. We need to know this
before we can do anything related to finding the right
pump.