- 2072 Chaitra · 8 marks
Resultant force on curved surface ABCDE (S = 1.25)
Short answer
With γ = 12.26 kN/m³, net horizontal force from the 4 m wall is 981 kN; vertical force is 2732.5 kN. Resultant 2903 kN at 70.3° below horizontal.
Find the resultant pressure force on curved surface ABCDE due to liquid with specific gravity S = 1.25, take length of the curved surface (normal to the paper) as 10 m. [Figure: free surface at A, vertical wall A-B 4 m, then curved portions with 2 m radii marked, vertical dimensions 4 m, 2 m, 2 m, 2 m, curve ends on the ground at E and C, D lowest point]
Resultant force on a curved surface = , where is the force on the vertical projection and is the weight of the liquid vertically above the surface up to the free surface.
Assumed geometry (the figure is not fully clear): A is at the free surface; AB is a vertical wall of 4 m; the surface then dips as a semicircular trough of radius 2 m from B to E through the lowest point D, so D is 6 m below the free surface. , m, kN/m³.
A |~~~~~~~~~~~~~~~~~~~~~~~~ free surface
| 4 m
B | E
\ R = 2 m /
'--. C .--'
' D ' D lowest (6 m)
Horizontal component
On the trough, the forces on the left and right quarters are equal and opposite horizontally, so they cancel. Only the wall AB (depth 4 m) gives a net horizontal force:
Vertical component
Volume above the trough = rectangle of 4 m depth over the 4 m width + half-disc of radius 2 m:
Resultant
Answer: kN, inclined at to the horizontal; kN, kN.
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