Answer:
F = 882.9 k N
Explanation:
given,
width of gate, W = 5 m
depth of the lake, h = 6 m
density of water = 1000 kg/m³
Atmospheric pressure = 101 kPa
now, Pressure at the bottom of the gate
P = ρ g h
P = 1000 x 9.81 x 6
P = 58860 Pa
Now, Force acting on the plate is
[tex]F = \dfrac{1}{2}Pwh[/tex]
[tex]F = \dfrac{1}{2}\times 58860 \times 5 \times 6[/tex]
F = 882900 N
F = 882.9 k N
the average horizontal force applied on the gate from the lake water is equal to F = 882.9 k N
