Textbook Example #1: Halliday and Resnick
(from Professor Halliday, by email)
In general, the flows above and below the card are not in the same flow stream. To the extent the flow expands radially, the the physics might violate the assumptions of constant average velocity and constant density.
First, the fluid velocity above the card is not constant, and there is no particular reason to take an average velocity.
Second, the fluid above the card does not flow, in a closed loop, around the bottom of the card, and back over the top of the card again. There is simply no closed-loop to link these two regions, so the claim that these two values must be equal, may have no basis.
Third, the fluid in the cylinder, at the center of the card has higher density than that at the open edge of the card, so the constant density provision may not apply.
The equation has force proportional to the square of the velocity. As such, there is no limit to the force [F], and it can be arbitrarily large. This, in turn, implies the pressure above the card can be arbitrarily small, even negative.