# What is the Force Exerted by a Falling Rod on a Hinged Support?

• member 428835
In summary, the conversation discusses a problem involving a rod attached to a hinge and a force acting on the rod to create constant angular velocity. The question is what force the rod is exerting on the hinge, taking into account the presence of fluid under the rod. Various approaches, including using Navier-Stokes and assuming a drag force, are considered. The assumptions of constant density and negligible viscosity and surface tension are made, and the potential impact of mass and friction at the hinge is mentioned. The final question is how to determine the pressure force of the fluid and its relationship to the hinge reaction and the applied force.
joshmccraney said:
$$F_n=\frac{4Fr^3}{3L^3}\cos{\theta}$$ Thank you both for the input!
Good, except lose the r^3 and the L^3

Chestermiller said:
The moment of the drag force is ##M=FL\cos{\theta}=\int_0^L{k'r^3dr}=k'\frac{L^4}{4}##
Question: Why is the upper limit of integration L? The drawing attached to post #16 shows the fluid extending only partially along the full length of the rod. Or is it just a drawing?

kuruman said:
Question: Why is the upper limit of integration L? The drawing attached to post #16 shows the fluid extending only partially along the full length of the rod. Or is it just a drawing?
That's not how I interpreted the diagram. I don't know what the correct interpretation is. Josh?

Yea, my drawing is imperfect. Fluid is coming out of the entire triangular region.

joshmccraney said:
The initial question posed was asking what force the hinge exerts on the ground.
There is no mention of the ground in the OP. Have you stated the problem word-for-word as given?

Not that I think I can contribute anything here, but I just wanted to understand the statement of the problem. I can't make any sense out of it whatsoever.

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