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Fluid mechanics and hydraulics miscellaneous

Fluid Mechanics and Hydraulics

  1. The force ‘F’ required at equilibrium on the semi-cylindrical gate shown below is
    1. 9.81kN
    2. 0.0kN
    3. 19.62kN
    4. none of the above
Correct Option: B

Taking horizontal & vertical components of hydrostatic forces
FH = ρ.g.h Aprojected

= 1000 × 9.81 ×
H
× (H × 1)
2

= 1000 × 9.81 ×
2
× (2 × 1)
2

= 19.62 kN/m width.
Fv = weight of water displaced
= Mg
= ρvg = ρg. v
= ρ.g
π
R² × 1
2a

= 1000 × 9.81 ×
π(1)²
× 1
2

= 15.41 kN/m width
Location of centre of pressure, h' =
2
H
3

=
2
× 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



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