Ask Question
2 December, 06:29

A semicircular plate with radius 8 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)

+3
Answers (1)
  1. 2 December, 06:53
    0
    If the square end is under water: 312271.92 N

    If the round end is under water: 262976.67 N

    Step-by-step explanation:

    We have to:

    P = ρ·g·d

    where:

    P is hydrostatic pressure, g is gravitational acceleration, d is depth, ρ is fluid density

    Force = hydrostatic pressure x submerged area

    F = PA

    You didn't specify the orientation

    If the square end is under water:

    F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (2-y) √ (64 - y²) dy ... from 0 to 2

    F = 19620 ∫ (2-y) √ (64 - y²) dy ... from 0 to 2

    The result of the solution of the integral is 15.916

    Thus:

    F = 15.916*19620 = 312271.92 N

    If the round end is under water:

    F = (1000 kg/m³) (9.81 m/s²) (2) ∫ (y - 3) √ (64 - y²) dy ... from 3 to 5

    F = 19620 ∫ (y - 3) √ (25 - y²) dy ... from 3 to 5

    The result of the solution of the integral is 13.403

    Thus:

    = 13.403*19620 = 262976.67 N
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A semicircular plate with radius 8 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers