Solution Found!
The 0.5-m-radius semi-circular gate shown in thefigure is hinged through the top edge
Chapter 3, Problem 3-136(choose chapter or problem)
The 0.5-m-radius semi-circular gate shown in the figure is hinged through the top edge AB. Find the required force to be applied at the center of gravity to keep the gate closed.
Questions & Answers
QUESTION:
The 0.5-m-radius semi-circular gate shown in the figure is hinged through the top edge AB. Find the required force to be applied at the center of gravity to keep the gate closed.
ANSWER:Step 1 of 7
The resultant hydrostatic force applied by glycerin is \(F_{R g}\),
\(F_{R g}=\gamma h_{c g} A\)
Where,
\(\gamma\) is the specific gravity of glycerin
A is the surface area
\(h_{c g}\) is the vertical distance of the centroid from the surface of the glycerin
\(F_{R g}=1.26 \times 9810 \times \frac{4 \times 0.5}{3 \times \pi} \times \frac{\pi \times 0.5^{2}}{2}=1030 \mathrm{~N}\)