Drawing or sketch?

What are you covering the culvert with?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

A culvert on a 17% slope will have very high flow velocities and supercritical flow. High velocities means pipe wall erosion is a possibility, especially if your flow has a lot of rocks, soil, and debris. Supercritical flow means that a radical decrease in the pipe slope downstream of the 17% reach will produce a hydraulic jump.
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Since I don't what your design flow or design material are, I decided to check this as an RCP culvert (Mannings n=0.013). Here are my results at selected depth ratios:

D/d --- Q --- V ----- NF

10% 12.4 cfs 18.9 fps 6.4
30% 116.0 cfs 36.6 fps 6.9
50% 296.1 cfs 47.1 fps 6.6
70% 495.9 cfs 52.8 fps 5.8
90% 631.2 cfs 53.0 fps 4.2

The American Concrete Pipe Association (concretepipe.org) says, on their FAQ page, "At velocities up to 40 feet per second, the severity of velocity-abrasion effects depends upon the characteristics of the bed load." (https://www.concretepipe.org/faqs/#:~:text=Q%3A-,W....) The ACPA Concrete Pipe Design Manual (https://www.concretepipe.org/wp-content/uploads/20...) says "Maximum Velocity. Tests have indicated that concrete pipe can carry clear water of extremely high velocities without eroding. Actual performance records of storm sewers on grades up to 45 percent and carrying high percentages of solids indicate that erosion is seldom a problem with concrete pipe." You should be able to find similar information for corrugated metal pipes, HDPE, etc., either through additional internet sleuthing or by contacting pipe manufacturers.

I don't like to see velocities that high (in the flat country of the San Joaquin Valley, it's not an issue) and I like to avoid supercritical flow when possible. For your slope, would a combination of flatter slopes and drop structures work? Regardless, it appears that laying concrete pipe on a 17% slope is not out of line according to the ACPA. I just don't like it.

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

slope anchors are recommended. trench plugs might also be a good idea
sump to capture sand and gravel is also recommended to minimize erosion
flatter slopes with drops might be a better option
steep down drains with cmp are fairly common, but expect a shorter than avg service life

Below is a rough sketch of the layout. The culvert is proposed to be 48" CSP, but will be seeing flows well under its capacity since it's a relatively small basin. The culvert can definitely be smaller, but the owner requested for it to be upsized a bit. This allows me to bury it a decent amount as well. The fill above will be native from the site and topped with a hefty road section. I was planning on upstream slope protection to the road, but it seems excessive with the flows it will see. I don't really see how it could develop any measurable headwater.

From my models of the drainage, I get the following results:

2YR Storm:
Q max = 1.84 cfs
d/D = .05
Max V (culvert) = 6.96 fps
Mat V (outfall channel) = 4.97

100YR Storm:
Q max = 6.85 cfs
d/D = .1
Max V (culvert) = 10 fps
Mat V (outfall channel) = 8.24 fps

It seems like the velocities aren't anything crazy, but they are within the "High abrasion" category for FHWA.

17.7% something to be worried about for slope anchorage?

Even at the 100-yr storm, you will hardly be taxing the hydraulic capacity of this culvert. A 36" might be a better choice.

Regarding anchors, the most common value I have seen for when anchors are required is >= a 20% slope. But, you should start with the local agency and find out what their design standards (if any) require. If they don't have any specific requirements, your pipe vendor may have a recommendation as well as a ready-made anchor system if you need it (which they would be glad to sell you). Since this culvert will be under a road and you are close to a 20% slope, you may want to be conservative and install a couple/a few anchors regardless of the requirements.

Estimating the slope of the downstream channel, I get a normal depth of around 0.1' for the 100-year storm. Hydraulically, this works, but please check local design standards to see if the there is a minimum freeboard requirement. You have 0.9', will that be enough?

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

Yes I agree. I've got a request to the client to move towards a 36". The 48" was their original request, but I don't think they realized how small of an area is actually contributing to this.

We did a pipe about the same size on a similar slope. We used RCP and dropped it out into a big concrete box with a concrete baffle to dissipate the energy at the outlet. However, our pipe carries irrigation water, so the sediments carried are minimal.

If there's sediments carried by the water for yours, you should consider a series of drop structures, or plan on using concrete and relining the pipe periodically. Using corrugated pipe will help slow down the velocity some, but not enough to prevent sediments from wearing through the steel fairly quickly.

Rod Smith, P.E., The artist formerly known as HotRod10