(a) A dam has the cross section shown in with tan φ = 4. Show that the resultant hydrostatic force R acting on the dam is given by where Z is the total water depth, as shown, ρ is the water density,...

(a) A dam has the cross section shown in with tan φ = 4. Show that the resultant hydrostatic force R acting on the dam is given by

where Z is the total water depth, as shown, ρ is the water density, g is the acceleration due to gravity, and S is the width of the dam. Show also that the horizontal distance from O of the line of action of the vertical component of R is given by 7Z/36.

(b) Calculate the horizontal and vertical components of the hydrostatic force of a dam with the cross section if the width is 600 m and the water depth is 30 m. What angle does the resultant force make with the vertical and at what depth does the horizontal component of the hydrostatic force act?