A clincher tire cannot be mounted on a tubular rim because the channel a clincher tire uses to grip the rim is not present on the tubular rim. Tubular rims are designed specifically for tubular tires, which are torus-shaped and glued to the rim. They don’t have any lips that are commonly found on clinchers. The tube is encased in the tire and it is completely sewn. So, it means if you want to fix a flat, you would have to cut the tire and patching the tube, and then sewing it back up.
On the other hand, clinchers are rims/wheels with a tube and then a tire is attached over the tube. Also, the bead of the tire is hooked under a lip on the rim. Clinchers are usually cheaper, easy to maintain, and can be easily repaired on the road. But they are heavier, have a higher rolling resistance and if you get a flat, you won’t be able to ride on it. I have written a whole article on clincher vs. tubular wheels so do check it out for in-depth information.
But what if you want to use a tubular tire on a clincher rim?
You can and it is possible but not recommended. Some people will say it is possible but possible doesn’t mean it is safe to ride and it will perform well. In my opinion, I would suggest that you don’t use a tubular tire on a clincher rim or vice versa. It may result in poor ride quality and can be dangerous. Poorly glued tires may roll off the rim as heat from the brakes melts the glue. Unless you are a pro cyclist, there is no reason to go with tubular wheels these days.
Some pros and cons of clincher and tubular wheels:
Clincher wheels are most common and they are the cheapest and simple option available. They are easier to patch on the road. Also, you don’t need to glue or stretch tires, etc. The major downside associated with clinchers is the lower ride quality. They are also heavier because you have a tube, tire, and clincher interface. Finally, if you flat, it is not an option to ride on it.
Tubular wheels, on the other hand, are much lighter than clinchers. They ride really well and if you flat, you can still ride on it for a little longer. The tire stays on the rim even it is flat but it requires proper gluing. But all these benefits come at a cost. The tubular wheel will are a little more expensive than clinchers and they are more difficult to maintain. Finally, patching on the road is not an option.