-
The force ‘F’ required at equilibrium on the semi-cylindrical gate shown below is
-
- 9.81kN
- 0.0kN
- 19.62kN
- none of the above
Correct Option: B
Taking horizontal & vertical components of hydrostatic forces
FH = ρ.g.h Aprojected
= 1000 × 9.81 × | ![]() | ![]() | × (H × 1) | |
2 |
= 1000 × 9.81 × | ![]() | ![]() | × (2 × 1) | |
2 |
= 19.62 kN/m width.
Fv = weight of water displaced
= Mg
= ρvg = ρg. v
= ρ.g | ![]() | R² × 1 | ![]() | |
2a |
= 1000 × 9.81 × | × 1 | |
2 |
= 15.41 kN/m width
Location of centre of pressure, h' = | H | |
3 |
= | × 2 = 1.33 m | |
3 |
= 0.424 m
Moment about hinge,
⇒ –FH × (h' - h) + Fv × x + F × 2/2 = 0
= – 19.62 × (1.33 – 1) + 15.41 × 0.424 + F × 1 = 0
∴ F = 0 kN