If a barrier is placed in a river or stream, the obstruction to the flow will initially cause the water to slow down as it flows past the barrier. This will result in an accumulation of water before the barrier. As the water accumulates before the barrier, the depth will increase and the resulting hydrostatic force on the barrier will increase. The resulting increase in the height of the flow would also increase the pressure before the barrier, and would therefore the pressure would push the water to flow around the barrier at a faster rate. Eventually, the flow would equalize when the flow rate around the barrier increases to be equal to the flow rate of the overall river.
First, the equations to predict the force on the barrier were derived here
Then, experimental calculations verified the equation as seen here