Flow estimation

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flow formula

Formula for approximating flow in canyons. (Read directions, use with caution!)

You’ve finally arrived at the canyon, you’re ready to put the wetsuit on. Is it the flow you thought it would be? If you immediately answered “Sure!” then I need you to slow down for a second! With a few simple measurements, we can actually come up with a subjective measure of the flow, which will give you your best possible idea of whether or not you’re about to make a huge mistake! It’s quick, simple, and you can do the math in your head. Here’s what you to do:

 

1: Forget what flow you expected the canyon to be at. The season numbers are a guessing tool. My gauge models are far from perfect. Even a gauge for that specific spot may have changed since you last looked at it. You are now in person, at the canyon, and are in your best position to say what the flow is, and if it is safe.

2: Find the most consistently shaped, evenly flowing, no-rocks-poking-out-of-the water stretch you can.

3: Measure the length (l) of this run in feet. You should be able to do this with your rope, and your arm lengths, like you do for drops.

4: Drop sticks at the top, in the center of the flow and time them on their way downstream. Do it 3 times, get a rough average for time (t). A stopwatch is nice, but counting (one thousand one, one thousand two…) is acceptable. If your stick gets stuck, don’t count that time, and try again.

5: Calculate surface water velocity (v). v = l / t

6: Measure the width of this run. (w) Same way you measured the length.

7: Measure the depth (d) of deepest part of the cross-section your stretch. If depth changes over the length, measure a few times, and get an average. It can be useful to take a measuring tape sometime and find out how high your knee is, to help. Or stick a rope in, pull it out, and estimate that way.

8: Calculate the estimated flow (f) in cfs (it’s simple!):  f = (w * d * v) / 2

9: Consider reasons why this flow is or is not accurate (see below).

 

It’s going to be helpful for you to know why this works. Here’s a simple explanation:

 

Imagine a cross sectional area of the creek. This area should equal width (w) multiplied by average depth (D).

 

So actual flow (F) will be equal to that cross sectional area, times the average water velocity (v).

F = (w * D) * v

Let’s assume that the cross sectional area is somewhat bowl shaped (it often is). A trapezoid where the third of either side slopes up evenly toward the surface.

shape1

For that trapezoid the average depth (d) is two thirds of the maximum depth (D).

D = .667 * d

 

We have surface velocity (we’ll call it V), not average velocity, v. Fortunately there is a correction factor that real science people use for that. For a cobbly bottom stream the correction is .8

v = .8 * V

 

Now all we have to do is put that together.

F = (w * .667 * d) * .8 * v

 

More simply…

F= .533 * w * d * v

Which is pretty damn close to

F = (w * d * v) / 2

Easy to remember, and you can do it in your head.

But let’s not forget step 9. Why might our estimate be inaccurate.

Well first, maybe our stream’s cross-section isn’t that nice bowl shape. What if the stream banks are vertical, an even depth straight across?

shape2

The cross-sectional area of this box is 50% bigger than our bowl! So, multiply your estimate by 1.5.

 

What if only one side is a steep bank?

shape3
This cross-sectional area is 25% bigger. So multiply by 1.25

 

What if it makes a V straight to the bottom?

shape4
This is 75% the size of our bowl, so multiply by .75. I image you get the point.

 
What else could be wrong? Well remember how I said the correction factor for surface velocity to average velocity was for a cobbly streambed? What if it’s smooth bedrock? That correction factor is 0.9. So, add another 10% (technically 12.5%, but we won’t be that accurate anyway) to your flow.

 

What if you didn’t find a particularly great run to measure in? The stream is filled with boulders, big eddies, weird hydraulics that keep catching your stick? Well, try measuring in a few different places, see what you come up with. Keep in mind that your measurement is less accurate. That’s about all you can do.

Also keep in mind that you need to do this at the right spot. If there are a tributaries into your canyon, you’re better off measuring at the bottom of the canyon. If you can’t do that, you’ll have to keep in mind that the flow will increase once those tributaries hit.

 

You absolutely must keep in mind that this is an estimate. Even if you find a good section of stream, and make accurate measurements, you’re still likely to be 25% off in either direction. So say you come up with 8 cfs, if you’re feeling confident, tell yourself 6-10cfs.

 

If you’re inexperienced, or didn’t find a great spot to measure, maybe you’re 50% off, and the flow is 4-12cfs. In that case, if 12cfs is higher than you would want to do the canyon, take some more time to consider. And I don’t mean to keep measuring until you get a flow that tells you what you want! You might think this sounds silly, but I promise it’s very tempting, and easy to do.

Sierra Canyons Preview: Waterflows

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This is a preview from the intro for a guidebook I’m hoping to have out sometime in 2021 on technical canyons in California’s Sierra Nevada. It’s in no way meant to tell you that you should or should not make any sort of choice. Also, if you’re keeping track, I am saying LITERALLY NOTHING related to crossing large swift water rivers, which is a completely different activity. 

Waterflows:

The canyons in the Sierra are not as narrow, deep, twisted or carved as the sandstone slots of the Colorado Plateau, however many people find them just as awesome, and worthwhile. Along with crystal clear emerald pools, the flowing water, beautiful as it is exciting and dangerous, entices us.

However, this is not to say that the canyons are not worthwhile at lower water. Even when the flows come down to a trickle, the pools often grow more brilliantly colored, and the jumps are easier to scout. Especially within social media circles, it has become common for people to use how high of flows they did a canyon at to measure their self worth.

Please allow me to tell you what your Instagram followers won’t: No one cares.

Just go play in the canyons. Enjoy the scenery. Have fun. Or, if there’s too much damn water, do something else. There are other canyons, or if that fails, there’s good breweries scattered about the Sierra as well.

I’m going to do the best job I can at helping you to forecast and assess the waterflow of these canyons. That said, it’s not easy, and it won’t be perfectly accurate. Likely you’ll be able to find evidence to support doing the canyon, even if it’s way too high. Don’t let the fact that you really really want to do the canyon alter your judgement. Listen to everyone’s input. Don’t just follow a single person’s lead. Don’t die!

Interpreting cfs (Cubic Feet per Second):

The best way we have to look at swiftwater conditions in canyons is cfs. If you think of the cross section of a river, or say, the lip of a waterfall, this is the volume of water that passes over that lip every second. The great thing about cfs, is that (disregarding tributaries), cfs is constant along a waterway.

However, what we are actually concerned with is the force that can be exerted on our bodies. One cfs of water equates to 28.32kg/s of mass. Mass per second is still just a measure of flow. This actual force is calculated by multiplying that 28kg/s by the change in velocity. If we assume your body is stopped in the water, then your velocity is zero.

So more simply flow times velocity is the force of the river. This means at 1 meter per second velocity, and 1 cfs flow, we have 28kg m/s2 of force, which is 28 newtons, or 6.3 pounds. Say we have a canyon with 5 cfs, flowing through a rapid that moves water at 10m/s. That’s 6.3*5*10 (315) pounds of force!

Fortunately, most of the time you are not facing the entire force of the water. In particularly narrow canyons, you might face most of it. That’s why 5cfs can be a lot for a narrow slot. However, in a wide canyon, you might only be hit with 10% of the water, and only 10% of the force. So different canyons can work at different flows.

Let’s think of another example. Say the canyon is flowing at 20cfs. You start at a pool, where it flows at 0.1meters/second. The force of the river here is 12.6 pounds. It’s calm, and doesn’t look intimidating. However, you get to the same rapid, which because of higher flows would move very fast, say 15meters/second. The river now has nearly a full ton of force behind it! It’s a raging torrent, and something you probably want no part of. This is a common problem with looking at the flow of canyons. They appear tame, until they are not. This is why it is super important to have an idea of the flow of a canyon.

You may think, what if a canyon only flows at 2cfs, but the water moves at 50m/s!? That’s 600 pounds of force! Is cfs completely useless? No it isn’t. The water will not be going that fast. A frictionless freefall of 100 meters would provide a speed of 44m/s. Water is subject to friction, and the less water there is, the more it tends to disperse, and the more it is slowed by air. I’ve heard people discuss formulating and deciding on what kind of force you get from what height drop and what flow, but I don’t think this is particularly necessary or useful. I can think of one waterfall, in Garden Creek in the Grand Canyon, where the ~2cfs of water flows down ~25meters down a chute that keeps it from dispersing. The result is water current powerful enough to take your feet out from under you, which if you’re confident at rappelling, is pretty funny. So, unless you are in something like a cave, and find yourself forced to take all of 1-2cfs directly to the face, these flows typically will not pose seriously problems given effect use of swiftwater canyon techniques.

So I argue that knowing just the water flow, and the general width/nature of the gorge, we can get a good idea of what reasonable flows are. Specific features are necessary to take into account, mostly when pushing the upper limits of reasonable flow.

Here’s a quick chart for reference. Imagine we have 3 types of canyons: Narrow slots like you find in Utah, typical Sierra Canyons that tend to be ~6-10 feet wide, and larger river gorges likes the East and Middle Forks of the Kaweah, that are less steep and typically over ten feet at even their narrowest points.

Please keep in mind that none of this is definitive. Specific canyons have specific features that can be more or less dangerous at different flows. For instance, if I (person who is semi-experienced with swift water canyons) were descending a canyon I had little to no information on, I would look for the flow to be in the Low-Moderate range.

Flow Narrow Slot Sierra Canyon River Gorge
2 cfs Moderate: Might hit hard, but should not be problematic. Low: Should not cause issues, and be appropriate for less experienced swiftwater canyoneers. Very low: Likely manageable with very little swiftwater experience.
4 cfs Moderate-High: Expect to get pounded by waterfalls and potentially swim or work against strong currents. Low-Moderate: Might hit hard, but should not be problematic. Low: Should not cause issues, and be appropriate for less experienced swiftwater canyoneers.
6 cfs High: Force of water may be prohibitive for rappelling. Strong swimming required to deal with eddies and hydraulics. Moderate: Rappelling directly in the current could prove difficult. Low-moderate: If channelized pourovers are avoided, things should still be easy.
10 cfs Extreme: Rappelling directly in flow, swimming through hydraulics, and avoiding being swept over drops will all prove risky. High: Force of water may be prohibitive for rappelling. Strong swimming required to deal with eddies and hydraulics. Moderate: Plan routes carefully at falls to avoid the strongest flows. Experience with swiftwater necessary.
15 cfs Don’t do it! Very high: Rappels should be directed out of flow. Risk of strong hydraulics and being swept over falls is very real. Moderate-High: A little more caution and experience required, but likely still manageable.
25 cfs Absolutely not! Extreme: Safety lines necessary above drops. Hydraulics and waterflow of falls must be avoided. Most Sierra Canyons are not descendable at these flows. High: Most often doable, but strong swimming by all participants, careful route planning, and swiftwater experience are required.
50+
cfs		 Certain death No! Extreme: Bypasses will need to be found for most drops. Strong swimming to cross current is likely necessary. Maybe doable by strong swimmers, experienced in swiftwater, in canyons they are familiar with.

 

Anyway, there are my thoughts on people and water moving through canyons in lovely harmony. I am by know means an expert on fluid dynamics, so if anyone wants to correct my physics, please do!

Coming next…? How to estimate cfs in a creek. It’s easy and it’s important! How much do you think is coming down the waterfall at the top of the page? Any guesses?