Hydraulics And Fluid Mechanics - Study Mode

Explanation

Solution: Understanding the Problem: We need to find the center of pressure on a rectangular surface submerged in water. The center of pressure is the point where the total hydrostatic force acts on the surface. Key Concepts: For a vertically submerged rectangle , the center of pressure (h cp ) is located below the centroid (center of area). The formula to calculate h cp is: h cp = h c + (I xx / (A * h c )) Where: h c is the depth of the centroid from the free surface. I xx is the second moment of area (moment of inertia) about the centroidal axis. A is the area of the submerged surface. Step-by-Step Solution: 1. Find the depth of the centroid (h c ): The rectangle's top is at 1.5 m and the bottom is at 6.0 m. The height of the rectangle is 6.0 m - 1.5 m = 4.5 m. The centroid is located at the middle of the rectangle's height. So, h c = 1.5 m + (4.5 m / 2) = 1.5 m + 2.25 m = 3.75 m 2. Calculate the Area (A): We are not given the width (b) of the rectangle so we consider it as b. Height of the rectangle h = 4.5 m A = b * h = b * 4.5 m 3. Calculate the Moment of Inertia (I xx ): For a rectangle about its centroidal axis, I xx = (b * h 3 ) / 12. I xx = (b * (4.5) 3 ) / 12 = (b * 91.125) / 12 4. Calculate the Center of Pressure (h cp ): h cp = h c + (I xx / (A * h c )) h cp = 3.75 + (((b * 91.125) / 12) / ((b * 4.5) * 3.75)) h cp = 3.75 + ((b * 91.125) / 12) / (b * 16.875) h cp = 3.75 + (91.125 / 12) / 16.875 (b cancels out) h cp = 3.75 + (7.59375 / 16.875) h cp = 3.75 + 0.45 h cp = 4.2 m Therefore, the correct answer is Option C: 4.2 m.