(b) A curved gate at the base of a \( 5 \mathrm{~m} \) wide wall retains water with a depth of \( 2.5 \mathrm{~m} \). The radius of the curved gate is \( 1 \mathrm{~m} \) as illustrated in Figure Q5b. Figure Q5b Calculate the magnitude and the direction of the force required to keep the gate in place. (8 marks)
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The hydrostatic pressure (P) at a depth (h) in a fluid is given by the formula: P = ρgh where ρ is the fluid density (for water, ρ = 1000 kg/m³), g is the acceleration due to gravity (g = 9.81 m/s²), and h is the depth. The centroid of the curved gate is Show more…
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A $2.5-\mathrm{m}$ -diameter gate is connected to a water reservoir as shown in Figure 2.61 . The gate is oriented at $35^{\circ}$ to the horizontal, the centroid of the gate is $1.5 \mathrm{~m}$ vertically below the water surface, and the weight of the gate is $500 \mathrm{kN}$. The gate is pin-connected to the reservoir at the top of the gate (at $\mathrm{P}$ ) and is opened by applying a vertical force at the bottom of the gate (at Q). (a) What is the magnitude of the resultant hydrostatic force and its location relative to the top of the gate? (b) What is the magnitude of the force required to open the gate?
A square gate $(4 \mathrm{m} \text { by } 4 \mathrm{m})$ is located on the $45^{\circ}$ face of a dam. The top edge of the gate lies $8 \mathrm{m}$ below the water surface. Determine the force of the water on the gate and the point through which it acts.
A $2 \mathrm{~m} \times 3 \mathrm{~m}$ rectangular gate is located on the sloping side of a water reservoir such that the $2-\mathrm{m}$ side of the gate is parallel to the water surface. The side of the reservoir (and the gate) slopes at an angle of $60^{\circ}$ to the horizontal, and the top of the gate is $2.5 \mathrm{~m}$ vertically below the water surface. Estimate the resultant hydrostatic force on the gate and the effective location of this resultant force, as measured vertically downward from the water surface.
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