In this screencast we will discuss the concept of the control valve, one of the most important
pieces of machinery in our control scheme. The control valve, as the name indicates,
is controlling the flow rate. It is often controlling the flow rate in a control scheme
of the value that we are manipulating in order to meet our particular control specification.
So as an example, if we were to talking about a heat exchanger, and we are trying to control
the temperature of our process fluid what we would be manipulating in order to get that
desired temperature is a flow rate of, for example cooling water. So to get a particular
outlet process fluid temperature that would correspond to, via using an energy balance,
a particular flow rate of cooling water. Thus its important that a control valve is able
to adequately control in the range of interest. This range of interest we dictated by the
process, so whether or not we would need fifty two to two hundred gpm of cooling water to
satisfy this, or twenty five to seventy five gpm would be dependent on the various specifications
of the process. The design equation for the control valve can be represented by the following
relationship, where q equals Cv multiplied by f, multiplied by the square root of delta
pv over g sub s. Now lets go through what each of these variables represents. Q represents
the flow rate of whatever fluid you have. Delta pv represents the pressure drop, its
not the entire pressure drop across the entire process, this is the pressure drop across
the valve only, and this can become important a little bit later on as you are trying to
appropriately size a valve. Gs represents the specific gravity. Cv represents the valve
coefficient, and the valve coefficient is an explicit definition. It represents the
amount of water that passes through a fully open valve when the pressure drop across it
is a standard value. Depending on your units this can be different, but typically one example
of a standard value would be one psi. The final value f is known as the valve characteristic,
and the valve characteristic is related to the lift of the valve. In other words, how
open it is, and in a simple way the valve characteristic can be represented as the ratio
of the actual flow rate going through divided by the maximum flow rate. So what we're going
to talk a little bit more about the lift in just a minute, but an important point to note
about this equation is that it is only valid for liquids. The reason why its only valid
for liquids is because of the fact that gasses being compressible that causes an issue with
the fact that we would need to know more information about the gas, particularly pvt information,
in order to appropriately size the valve. Where as in this equation here we are assuming
incompressible liquids, so therefore it doesn't really matter the type of liquid we have,
nor its temperature and what not. So broadly there are three categories of valves we have:
linear, equal percentage, and quick opening valves. These three valves are differentiated
by how their flow rate is related to the a for mentioned variable of the lift, which
is a representation of the fraction open the valve is. So a lift of zero would indicate
a fully closed valve, and a lift value of one would indicate a fully open valve. So
for linear valves they are designed such that the flow rate is directly proportional to
the lift. In other words how open it is for a constant pressure drop. So therefore as
you double the openness of the valve, you go from forty percent open to eighty percent
open, you are doubling the flow rate going through. So what this means is the fact that
the valve characteristic f is proportional to l, the lift. So where this l here represents
the value of the lift. For the case of equal percentage we have the case where there is
an equal percentage in change in flow for a particular change in the lift. So in other
words what that is saying is the fact that df dl is proportional to f. And another way
to say this also is the fact that f equals r raised to the lift minus one, just as an indication
here this represents the lift, which in some textbooks can be represented by a cursive
l, where r is a constant parameter that is a particular aspect of the valve you are using.
Finally quick opening valves are done such that the valve characteristic f is related
to the square root of the lift. For a quick opening valve what we want, as the name indicates,
is when we open the valve very slowly a lot of flow comes out. Therefore these valves
are designed such that at low flow rates you get more of the flow coming out, and then
when the valve gets more open you get more of a diminishing returns on it. Because of
this rational quick opening valves are used for safety only and are not used for controlling
systems because of this setup of trying to have very high amount of flow very quickly
it makes it very difficult to control it at these very low openness values. So in this
screencast we have discussed some of the important information as related to control valves.