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By Thomas Gail Haws, P.E.

Pressure slope is the continuous loss of pressure due to friction in a long uniform (prismatic) channel, like a ditch or a pipe. It can be calculated as total pressure loss divided by length.

For example, in a long, sloped, open, freely flowing irrigation ditch, the water surface drops a bit every meter. Because the flow is uniform, friction takes away the exact amount of energy that gravity gives, and the water neither speeds up nor slows down. Or in a long pipe connecting two reservoirs, the difference in elevation between the reservoirs gives pressure to the pipe that is used up evenly foot by foot to push the water against roughness friction in the pipe.

We can calculate pressure slope in a pipe very easily. We simply add up all our pressure sources (usually gravity and pumps), then subtract any pressure losses like at valves, bends, expansions, and contractions, and finally divide the remaining pressure by the length of pipe we have to push through. Yikes!

But we can simplify more.

If a pipe is really long, or there are no pumps, valves, bends, or anything, all we have to do is divide the gravity pressure by the pipe length, which looks a lot like the pipe slope if the water level all along the pipe is pretty much at the top of the pipe.

So, can you use pipe slope instead of pressure slope?

You can use pipe slope for pressure slope (friction slope) in the following cases:

- Long, straight pipe, not full
- If your pipe is flowing only partially full and is straight and long (?) enough that the water surface is simply parallel to the pipe bottom, then the pipe slope is the same as the friction slope. For practical purposes, most pipes are long.
- Long, straight pipe, no end submergence
- If the incoming and outgoing water level at each end of your pipe is no higher than the top of your pipe there, and if the pipe is long (?), then the pipe slope is the same as the friction slope.

If you can't use the pipe slope for friction slope, you may be able to use one of the following cases:

- Vertical bend(s), long flat upstream segment, not full
- If your pipe is flowing only partially full and has a flat upstream segment long (?) enough that the water surface is simply parallel to the pipe bottom, then the upstream flattest pipe slope is the same as the friction slope.
- Long submerged pipe with or without vertical bends
- If your entire pipe is long (?) and lower than ponds at the two ends, ignore the pipe slope. The difference between the pond elevations divided by the pipe length is the friction slope.
- Long partially submerged straight pipe
- If the outlet of your pipe is unsubmerged or is in a pond that is lower than any parts of your pipe, and your pipe is straight, ignore the pipe slope. The difference between the upstream pond elevation and the downstream pond elevation or pipe end, whichever is higher, divided by the pipe length, is the friction slope.
- Long partially submerged pipe with bends
- If your pipe is only partially submerged and has vertical bends, you are on your own. Choose a flow and check that there is enough total pressure (head) to push that flow through the added lossess from each pipe segment. Remember that the water surface can't go below the top of pipe. You may need to ask an experienced engineer to check your calculation.

For practical purposes, most pipes are long. But at the ends of all pipes, flow may be speeding up, slowing down, deepening, shallowing, swirling around, and all kinds of untidy stuff that isn't covered by friction slope equations. This causes what we call point losses because we imagine them as happening at a point instead of along a pipe. If your pipe is so short that its flow never settles down, friction slope equations mean nothing, and point losses are everything. Also, even if your pipe is long, you may need to somehow account for the losses at the ends. If you aren't sure whether the losses at the ends of your pipe may change your design decision, you probably should use a pipe head loss calculation instead of a pipe flow equation based only on slope.

Why use a head loss equation? A head loss equation lets you use "minor loss coefficients" to stay out of trouble by throwing in some rough guesses about what's happening at the ends or at any bends.

How do you know if you need to account for minor losses? First, it never hurts to use a pipe head loss equation with a point (minor) loss coefficient of at least 1.5 (you could conceptualize the 1.5 as 1 velocity head of loss at the pipe exit and 0.5 velocity heads of loss at the pipe entrance of a straight pipe). Second, compare the velocity head to your total height drop (called head) from one end of your pipe to the other. If the velocity head lookes insignificantly small to you, then point (minor) losses (at least 1.5 times and probably less than 2 to 10 times the velocity head) may be insignificant also. But if velocity head looks like it's a significant piece of your available drop (head), you probably want to include end losses in your design calculation. Use a minor loss coefficient reference (or throw in 0.5 for every 45 degree bend, 1.5 for every 90 degree bend, and 1.8 for tee junctions) to get your estimated point losses in the right ballpark, but don't sweat the precision.