Question

(2.4) Example 1 The figure left shows a triangular cell in a 2-d unstructured mesh, p-9 (0,2 p-7 p together with the coordinates of its vertices and the average pressures on the cell faces. Calculate the x and y components of the net pressure force on the cell (per unit depth). p-5 (4,0) The net pressure force component in the x or y direction on a face is given by: pressure x projected area into the cell. Hence, Jace faces

Answer 1

For the face with p = 5, we have $\Delta$ x = 4 - 0 = 4 and $\Delta$ y = 2 - 0 = 2

For the face with p = 9, we have $\Delta$ x = 2 - 0 = 2 and $\Delta$ y = 4 - 2 = 2

For the face with p = 7, we have $\Delta$ x = 4 - 2 = 2 and $\Delta$ y = 4 - 0 = 4

Net Force F_x = Sum of -p $\Delta$ y for each face

F_x = 5 * 2 + 9 * 2 - 7 * 4 = 0

Net Force F_y = Sum of p $\Delta$ x for each face

F_y = 5 * 4 - 9 * 2 - 7 * 2 = -12