How can you determine the pressure drop, also known as pressure loss or ΔP1, of a piece of straight pipe?
Any fluid mechanics textbook will describe in detail the process you can use, the reasons why it works, and the history of how people discovered the equations. This post will skip the background, and just go over the steps quickly, with some links to a charts and calculators and some practical advice.
We will assume it is completely straight pipe with fully developed flow. There are no eddies or fluctuations due to valves, fittings, pipe entrances or exits, etc.
If you want to consider bends, entrances, and exits, there are many different methods not discussed here. The most popular is the equivalent length method in Crane Techinical Paper No. 410. If you have changes in elevation or pipe size apply Bernoulli's principle.
Straight pipe steps:
Although the order is a little flexible, you should hit on all of these steps to size your pipe:
- Determine the “pipe specification” or "pipe spec": this is a set of instructions set up by your company that tell what material the pipe is made of, and what "schedule" (thickness) the pipe is. The pipe spec chosen in any design depends on metallurgy (matching material to the fluid inside), corrosion/erosion, and other factors. Choosing the correct pipe spec is a topic in and of itself and is beyond the scope of this post. If you're not working with a list of pipe specs to choose from, determine the pipe schedule and material yourself at this step. If you have no idea at all, Schedule 40 carbon steel pipe is the most common in many industries.
- Look up the pipe roughness of your material in a pipe roughness table. If the pipe is not new, consider looking up a roughness factor for old pipe. Be careful to watch the units of this roughness value.
- You need to determine the “nominal pipe size”, i.e. the named size that everyone refers to. (If you are designing a new pipe, you have to start by guessing the nominal pipe size). Then, use the pipe spec from step 1 to look up the "pipe schedule". Use the nominal pipe size and pipe schedule with a standard pipe table to determine the Internal Diameter (ID) of the pipe, and it’s internal area. For example, a 4” schedule 40 pipe is really 4.026” ID. (4.5” outer diameter – 2 x 0.237” pipe thickness).
- Determine the density and viscosity of your fluid at the flowing temperature and pressure. There are many ways to figure this out: maybe the use tables of values (such as "steam tables"), or measured values from the lab, or a process simulation software tool. If you are worried that large changes in temperature or pressure inside the pipe could significantly affect the density and/or viscosity values, see the note at the bottom of this post.
- Calculate the Reynold’s Number and determine your flow regime.
- Calculate the Friction Factor. Be careful, as there are several values of the friction factors floating around that are multiples of each other. The different disciplines of engineering tend to use different friction factors. So just make sure the friction factor you use goes with the pressure drop equation you use. This is a good reason to have a fluid mechanics textbook and use the same book all the way through.
- Determine the flowrate you want to use in the calculation. Normally, depending on the purpose of your calculation you’d want to consider either the normal flowrate (what the pipe sees most often) or the design flowrate. For the design flowrate, take the highest flowrate the pipe will carry in any operation mode, and then add some factor of safety on top. +10% is common, but +20% if often used if you expect a lot of fluctuations due to controls. (e.g. reflux around distillation columns, pipes that help provide level control to a small drum).
- Knowing the flowrate going through the pipe (from step 7) and the area of your pipe (from step 3), determine the velocity of fluid in the pipe: volume of flow/time divided by area
- Determine the length of your pipe. Preferably from field measurements or pipe isometric drawings, but if not estimate using the plot plan
- Use the D'Arcy-Weisbach Equation to determine the pressure loss. There are many forms of this equation, so you can find one that works conveniently with the units you are using.
- Compare the pressure loss and velocity you calculated to a table that lists reasonable values for your application. Most major companies have their own tables based on their experiences and preferences, and most tables are intended for use with the normal (rather than the design) flowrate. If you find that your pressure drop or velocity values are violating the table, use your judgement to determine if that's really a problem. Maybe you should reconsider the size chosen in step 3. (Normally you select a reasonable velocity to avoid non-flowing fluid getting caught in a slow spot in the pipe, or to avoid erosion due to excessive velocity. The pressure loss guidelines help you strike a balanced between oversized pipes, which are expensive to buy and install, and undersized pipes, which require large pumps and compressors to move fluids. This is to balance capital vs. operating cost). If you are doing a revamp where you redesign a plant and make use of existing piping, it often pays to bend the rules instead of ripping things out and installing new pipes. Maybe you can tolerate a higher pumping cost or quickly eroding pipes if it will let you reuse existing piping for awhile.
- Calculate the static head effect due to any change in height
- Using the pressure change from steps 10 and 12, ensure there is enough pressure at the start of the pipe to actually get the fluid through the pipe. Normally you'll want to check this at the rated flowrate
What if conditions in the pipe affect the calculation?
In step 4 we assumed that just one density and one viscosity value apply over the entire pipe. Often this isn’t accurate. For example, gas density depends strongly on pressure, and you lose pressure as you flow through a pipe! Temperature changes can affect viscosity and density in liquids and gases. If you have thick oils or molten sulphur flowing through a pipe and the fluid is cooling, viscosity can vary tremendously. How do you deal with this?
In some cases it might be possible to set up equations for everything and use integration to solve it. But almost everyone does it the “hack” way: you break the pipe up into several “segments,” which are small lengths of pipe inside the total pipe you are studying. I might break up a 100ft pipe into 10 segments, each 10ft. Determine the density and viscosity at the inlet of the pipe, and assume these properties remain constant throughout the first segment. Determine the pressure drop for the first segment. Now, I know the pressure at the second segment. Calculate the properties at the start of the second segment, and assume they remain constant throughout the second segment. Now the pressure at the entrance to the third segment is knwon. And so on.
Make enough segments so that your assumption of constant value doesn’t impact your accuracy. (For example, for gases, a common rule of thumb is that if you lose less than 10% of the total pressure of the gas in a pipe segment, you can assume one constant density over the segment and still have acceptable accuracy). Note that you’ll want to consider the static head in each segment. The more segments you use the longer it will take but the more accurate you will be.
All the commercial programs that I have seen use segments. They usually have an option to change the number of segments. (More segments = more accurate, but longer to calculate).
Shortcuts you can try:
- There are many programs you can buy that will do some of these steps for you. There are dedicated hydraulics programs. Also, many process simulators have pipe segment tools which are OK if you have only a few lines to study.
- There are many online calculators that will do some of these steps for you. I may link to some later.
- You may be able to find tables of calculated values, especially if you have air or water in a standard pipe size. My copy of Crane Techinical Paper No. 410 has this, along with ways to quickly adjust the air table for different temperatures.
What about choosing a pipe spec? Knowing good flowrate and pressure loss values? Dealing with two phase flow? Or branching flow? Or fittings?
These issues are complicated enough to be their own topics.
Updates to this post:
2009-08-19 - Improved the clarity of many sentences.
2009-10-20 - Linked the reference of Crane Technical Paper 410 to a post about it.
2010-01-16 - Added note about Bernouli's principle being required to model elevation changes and pipe size changes.
2010-08-14 - Expanded description of pipe specs in step #1.
2010-11-15 - Suggest that in step #1, carbon steel schedule 40 pipe is quite common and makes a decent "first-pass" assumption.
- Tip: for some fonts you can hold ALT and type 916 to automatically create the “delta” sign, Δ. Δ is often used to mean “difference” in math/science/engineering. [↩]