Let’s talk about throttling valves, another type of steady flow device. A throttling valve is any
device that restricts the flow of a fluid and reduces the pressure of the fluid. So a common
one you probably seen before are adjustable valves. Previously, we talked about turbines
where they create a pressure drop but that involved work output. In a throttling valve,
this pressure drop happens without any work interactions. When the pressure drops, there is
usually a temperature drop in the fluid as well. Let’s discuss the characteristics of these valves.
Remember that for a steady flow device, our energy balance equation says
that the rate of energy in must equal the rate of energy out. We can expand this equation like this
to account for all the types of energy associated with steady flow systems. If we have a throttling
valve system like this, the heat transfer between the system and the surroundings are negligible.
That’s mainly due to the device being small, not enough time or a large enough area for
heat transfer. Again, the heat transfer between the system and the surroundings are negligible
but a temperature drop in the fluid is still possible. However, when it comes to ideal gases,
the temperature remains constant. There are no work interactions so work is zero. The change in
potential energy is also very small, so small that it’s negligible. And generally, with throttling
valves, the velocity at the exit side tends to be higher than the inlet side. But when you look at
the big picture, its simply insignificant for our purposes, so kinetic energy is negligible.
Now all we are left with is this, so mass flow and enthalpy. Now normally in a throttling valve,
we have one inlet and one outlet, which means mass flow will be the same.
So we can cancel it out and we are left with this. In simple terms, the enthalpy value at the inlet
is equal to the enthalpy value at the exist of a throttling valve.
Now let’s cover a few examples to see how we can use what we just learned.
In this question, we are told that there is a saturated liquid
mixture of water that’s throttled down. We need to figure out the quality of steam in the line.
If you forgot what quality is, it’s the ratio of the amount of vapor to the amount of liquid
in a system. If you need a refresh, please see the description. Let’s write down what we know.
The initial pressure is 1500 kPa and the final pressure is 50 kPa.
We don’t know initial temperature but final temperature is 100 degrees Celsius.
Let’s write our energy balance equation. Energy in is equal to energy out. Since this is a throttling
problem, kinetic energy and potential energy are negligible, the heat transfer in and out
is negligible, and work is also negligible. So our energy balance equation becomes this. Our
equation is simply initial enthalpy is equal to final enthalpy. We can find this enthalpy value
using a table since we have both the pressure and temperature for the exit side. So our pressure is
50 kPa and temperature is 100 degrees Celsius. Our value is right here. Remember, this enthalpy
value is the same at the inlet of our throttling value. Now let’s write down the equation for
quality. So to find the quality, we need these 2 values. We can find them on a pressure table.
For this, we can use the pressure at the inlet side, which is 1500 kPa. So the values we need
are these. All that’s left is to plug these values in and solving gives us a quality of 0.944.
In this example we have refrigerant-134a being throttled, and we need to figure out the
temperature drop during this process and the final specific volume. Let’s write down what we know.
The initial pressure is 700 kPa and final pressure is 160 kPa.
Now we can write our energy balance equation. Since this is a throttling valve, kinetic energy,
potential energy, and work interactions are all negligible. We can figure out the initial enthalpy
and initial temperature using a refrigerant table. So let’s look for 700 kPa. Remember, we are told
that it’s a saturated liquid so the saturation enthalpy value is right here, and here is our
saturation temperature, which is the temperature of the fluid at the inlet of the valve.
Now we need to look at the table for a pressure of 160 kPa. Note these values here,
which tell us the saturated liquid enthalpy value and saturated vapor enthalpy. Okay,
now we know our initial enthalpy is equal to final enthalpy. Notice how our final enthalpy value is
less than the saturated vapor enthalpy but greater than the saturated liquid enthalpy. That means our
refrigerant is now a saturated mixture at the exit side of the valve. So if we go back to our table
and look at the saturated temperature of the refrigerant, we see that it’s -15.60 degrees
Celsius. All that’s left for us to do is find the difference and we get our temperature drop.
The next part of the question wants us to figure out the final specific
volume of the refrigerant. To find it, we can use this equation, which is just using the quality
to figure out specific volume. So we need to find a bunch of things. We will start off with finding
the quality. For that we can use this equation. We have a lot these values, we just need this one.
We can find it from the table at 160 kPa since that’s the final pressure. The value
we’re looking for is right here. Okay, let’s plug our values
in and solve for the quality. Now we have the quality, but we are still
missing these 2 values. These, we can find from the same table, so again, pressure is 160 kPa.
Here are the 2 values we need. Remember that this is just the difference between saturated
vapor and saturated liquid specific volume. We have everything we need,
so let’s start plugging in values. Solving tells us the final specific volume of the refrigerant.
In this problem, we have steam being throttled and we have to figure out the final temperature
of the steam. Let’s write down what we know. The initial pressure is 8 MPa,
and the temperature is 350 degrees Celsius. After being throttled, the pressure is now 2 MPa.
So as usual, we write our energy balance equation and since this is a throttling valve,
we know that it simplifies to initial enthalpy is equal to final enthalpy.
We can figure out the enthalpy value using a steam table.
Our pressure is 8 MPa, and the temperature is 350 degrees Celsius. Here is our value.
Now we know at the exit side, the pressure is 2 MPa, and we also know the enthalpy value,
since again, h1 is equal to h2. So looking again at a steam table, here is 2 MPa,
and the enthalpy value is between these 2 values. That means to find the temperature, we will need
to extrapolate or use the link I provide in the description below, where you can enter your
values and find all the different properties you need for steam. So we get 286 degrees Celsius
and that’s our answer. That should cover the types of problems you will
face when it comes to throttling valves. Thanks for watching and best of luck with your studies.