The document contains 5 problems involving calculating forces on gates, hatches, and other structures located in reservoirs, tanks, and underwater. The problems involve determining the resultant force of water, the moment needed to open a gate, the minimum air pressure to open a hatch, the mass required to open a gate at a certain water height, and the minimum force needed to support a rectangular gate. Diagrams and equations are provided for the solution to each problem.

1. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (1)
Tutorial (4)
1- The 4𝑚-diameter circular gate of the shown figure is located in the
inclined wall of a large reservoir containing water (𝛾 = 9.8 𝐾𝑁/𝑚3) the
gate is mounted on a shaft along its horizontal diameter, and the water
depth is 10 𝑚 above the shaft.
Determine
 The magnitude and location of the resultant force exerted by the water on
the gate.
 The moment that would have to be applied to the shaft to open the gate.
Solution

2. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (2)
𝛾
𝑁
𝑚
∑
𝑁 𝑚

3. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (3)
2- A structure is attached to the ocean floor as shown in the Figure. A 2𝑚
diameter hatch is located in an inclined wall and hinged on one edge.
Determine the minimum air pressure 𝑝1, within the container that will
open the hatch. Neglect the weight of the hatch and friction in the hinge.
Solution
𝑚⁄
𝛾
𝑚
𝑁

4. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (4)
𝑚
𝑚
∑
𝑝
𝑝

5. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (5)
3- The flow of water from a reservoir is controlled by a 1.5 𝑚 wide L-shaped
gate hinged at point , as shown in the figure. If it is desired that the gate
open when the water height is 3.6 𝑚, determine the mass of the required
weight 𝑊.
Solution
𝛾
𝑚
𝑁

6. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (6)
𝑚
∑

7. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (7)
4- A 3𝑚 wide, 8 𝑚 high rectangular gate is located at the end of a rectangular
passage that is connected to a large open tank filled with water as shown
in the figure. The gate is hinged at its bottom and held closed by a
horizontal force 𝐻 located at the center of the gate.
Determine:
 The magnitude and location of the resultant force exerted on the gate by
the water.
 The minimum force 𝐻 required to support the gate.
Solution

8. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (8)
𝛾
𝑁
𝑚
∑
𝑁

9. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (9)
5- Determine the minimum Air pressure 1 required to hold the semi-
circular gate closed on this emergency dumb system.
Solution
𝛾
𝑚
[ ] ( ) 𝑁

10. Tutorial (4) Dr.waleed, Mob. 0100 4444 149 Page (10)
𝑚
∑