2. (35 points). The flow of water (p= 1000 kg/m³) from a reservoir is

controlled using a 5 m by 7 m rectangular gate. The gate is hinged at

point A as shown in the schematic, and a torsional spring with a spring

constant of 1.15 x 10³ kN-m/rad is used to keep the gate closed and prevent

water from leaving the reservoir. Under equilibrium conditions, the gate

makes an angle of = 10° with the vertical.

(a) Determine the height h of the water filling the reservoir. Assume

that the dimension I in the figure measures 5 m.

(b) Compute the net horizontal force acting on the hinge at point A. Is it

safe to fill the reservoir with the height of water computed in part (a)

if the maximum allowable horizontal load for the hinge is 8000 kN?

B=800

h

а= эм

0 (0°

S

16

مار

1-00 = 100

FR

Figure 2: Reservoir and gate equipped with a torsional spring.

1=5M

h = l + d

d = Sin as

d

S=

sin m

FR = (Ps (S+b) sin() ab

+

6²

12[5+&}

YP= ste

stb

AB= 800

S

EMA== NO +5n (YP-5) = 0

b-5M,

l=sm

B = 800, h = 1.15 x10³ UN-M/ cad

1

J

0 = 10⁰

B=80°

d

FR

8=100