Two-thirds of x m high, 10 m wide rectangular plate emerged in the freshwater channel, as shown in the figure. The plate is hinged about a horizontal axis along its upper edge through point A and is restrained from opening by a fixed ridge at point B. Determine the hydrostatic force in kN. P.S: The drawing is not drawn on an accurate scale.Here, x=9 m
Question
Two-thirds of x m high, 10 m wide rectangular plate emerged in the freshwater channel, as shown in the figure. The plate is hinged about a horizontal axis along its upper edge through point A and is restrained from opening by a fixed ridge at point B. Determine the hydrostatic force in kN. P.S: The drawing is not drawn on an accurate scale.Here, x=9 m
Solution
The problem seems to be missing a figure, but based on the description, we can calculate the hydrostatic force on the submerged part of the plate using the formula for hydrostatic pressure:
P = ρgh
where:
- P is the hydrostatic pressure,
- ρ is the fluid density (for freshwater, this is typically 1000 kg/m³),
- g is the acceleration due to gravity (approximately 9.81 m/s²), and
- h is the height of the water column above the point in question.
In this case, the plate is submerged to a depth of two-thirds of its height, so h = 2/3 * 9 m = 6 m.
Substituting these values into the formula gives:
P = 1000 kg/m³ * 9.81 m/s² * 6 m = 58860 Pa = 58.86 kPa
The total hydrostatic force on the plate is then given by the pressure times the area of the plate:
F = PA
The area of the plate is 10 m * 9 m = 90 m², so:
F = 58.86 kPa * 90 m² = 5297.4 kN
So, the hydrostatic force on the plate is approximately 5297.4 kN.
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