I know that in wider regions velocity of river is less than that in narrower region. This suggests that we should cross the river at the wider region. But at wider regions pressure is more due to the Bernoulli's equation and hence more force leading to more damage. This suggests that we should cross the river at the narrower region. This leads to a contradiction. So what is the correct choice? Or does it depend on other factors also?
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Presumably you mean crossing a river by foot. I have done this many times so here is an answer from the practical point of view: I always chose the widest shallowest region I could find. You want the water to move slowly so it does not push you that much: $F \sim v^2$. And you want it to be shallow so (a) there is not that much of an area against which it can push and (b) buoyancy does not become an issue. What you really care about is not falling into the water. You do not care how wide the crossing is as long as you can make all the steps safely. Anything more than knee deep can become dangerous very fast.
Regarding the Bernoulli equation - keep in mind that a river is an open channel. If the water pressure rises for whatever reason the water will simply rise up - the pressure near the surface will be the same (~ equal to atmospheric pressure) regardless of how fast the water flows.
Karel
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In general, it is safer to cross a river in wider, shallower regions of a river (see guides from, for example, US Fish and Wildlife, Bushwalking Victoria or New Zealand's Wilderness Magazine), though you should also note the other considerations and maybe also ask on a more field specific site, like the Outdoors SE sister site if you really are considering crossing a river. However, the reason you are getting an unexpected result is because Bernoulli's principle isn't really the appropriate way to model this, or at least, not without much more attention to detail.
The "pressure" referred to in Bernoulli's principle is the static pressure (see, e.g., this question on the difference), which, together with the dynamic pressure and potential energy is constant (ignoring losses due to non-conservative forces such as friction) due to conservation of energy. Notably, the net force applied by static pressure on a body in the water is zero, as it is the same in all directions. The force applied to an object in the water is a function of the dynamic pressure, the flow of the water.
Of course, one way to model this, is that any obstruction in the water would slow the flow of water in one direction, or even stop some streamlines completely, and therefore increasing the pressure on one side (producing a net force) but this is a more complicated way of doing things than would really make sense. Especially if you want to model a whole river, lots of change in height (potential energy), friction everywhere... you don't really need to go through all that to estimate what drag forces are going to be like
A related concept is the stagnation pressure, or "total" pressure of the fluid (see, for example, this resource page from eFluids). Essentially, if the flow of the fluid is forced to come to a stop entirely, the pressure at the "stagnation point" is equal to the sum of the static and dynamic pressure.
TL;DR: Pressure doesn't actually do anything to you in this situation, and you really need to account for more factors if you want to use Bernoulli here.
timuzhti
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