Example 2.7 Find the magnitude of the resultant force on this vertical wall of a tank which has oil, of relative density 0.8, floating on water as shown
Draw the pressure diagram as shown to the right. Solution Draw the pressure diagram as shown to the right. The resultant force (per unit length) is simply the area of the pressure diagram. It is convenient to split the area into three, and sum the answers. F1 = A1 = (0.8 x 103) x 9.81 x 0.8 x 0.8x0.5 = 2511.36 F2 = A2 = (0.8 x 103) x 9.81 x 0.8 x 1.2 = 7534.08 F3 = A3 = (103) x 9.81 x 1.2 x 1.2 x 0.5 = 7063.20 R = F1 + F2 + F3 = 17108.64 N/m R acts horizontally through the centroid of the pressure diagram.
Example 2.8 Find the magnitude and direction of the resultant force (in N not N/m) of water on a quadrant gate as shown below
At an angle Horizontal force, RH = Force on projection of curved surface on to a vertical plane = 0.5 x rgh2 x width = 0.5 x 1000 x 9.81 x 12 x 3 = 14715 N Vertical force, RV = weight of fluid above surface = rg x Area covered = 1000 x 9.81 x(pr2/4) x 3 = 23114 N Resultant force At an angle
Example 2.8
Solution
Last Semester First Exam
Fluid dynamics and its applications
Streamline & Pathline