Calculation for the location of support of vertical circular gate

Problem
A vertical circular gate in a tunnel 8 m in diameter has oil (sp. gr. 0.80) on one side and air on the other side as shown in Figure HD-73. If oil is 12 m above the invert and the air pressure is 40 kPa, where will a single support be located to hold the gate in position (above the invert of the gate)?
 

1994-may-hyd-tunnel-gate.jpg

 

A.   1.36 m C.   3.24 m
B.   1.84 m D.   2.62 m

 

Circular Gate with Water on One Side and Air on the Other Side

Situation
The figure below shows a vertical circular gate in a 3-m diameter tunnel with water on one side and air on the other side.
 

002-submerged-circular-gate.jpg

 

  1. Find the horizontal reaction at the hinge.
    A.   412 kN
    B.   408 kN
    C.   410 kN
    D.   414 kN
  2. How far from the invert of the tunnel is the hydrostatic force acting on the gate?
    A.   1.45 m
    B.   1.43 m
    C.   1.47 m
    D.   1.41 m
  3. Where will the hinge support be located (measured from the invert) to hold the gate in position?
    A.   1.42 m
    B.   1.46 m
    C.   1.44 m
    D.   1.40 m