A 4m diameter circular gate, mounted on a shaft along its horizontal diameter, is located on an inclined wall of a large reservoir containing water
. For a depth of 10m above the shaft determine, 1. the magnitude and location of the resultant force exerted on the gate by the water, and 2. the moment that would have to be applied to open the gate.HYDROSTATIC FORCE ON A GATE
May want to check out:
HYDROSTATIC FORCE ON PLANE SURFACE
ARCHIMEDES' PRINCIPLE
Similar to:
VIDEO LECTURE
COMMENTS
Feel free to leave any comments on the lesson - your views, improvements, mistakes, clarification of concepts, or vote to have this lesson revised. |
LESSON
This is a fairly straightforward problem of using the formulas to find the magnitude and location of the hydrostatic force and then taking moments about a point. Our problem is illustrated below:
Magnitude of force is given by
using vertical distance from the fluid surface to the centroid of the area given by 10m, it follows that
To find the location of the force, or center of pressure, through which
From our coordinate system,
and the distance along the gate below the shaft to the centre of pressure is
We shift our attention to the moment created by the respective forces. The moment required to open the gate is facilitated with the help of a free-body diagram. W is the weight of the gate and
and therefore
The moment required to open the gate is All information presentated, less questions and exercises, is original content of Donny, with slight references to various books.
Video courtesy of YouTube.com service. |
, 
acts, we use equations
since the area is symmetrical, and the centre of pressure must lie along the diameter A-A. To find 
, we use the standard results of moment of inertia,
and 
are the horizontal and vertical reactions of the shaft on the gate. Summing moments about the shaft,
, the moment needed to oppose the one from the hydrostatic force.
