Officer Aptitude Rating (OAR) Formulas Practice Test

Work in a fluid-piston system comes from the force the fluid pressure exerts over the piston and the distance the piston moves. The fluid pushes with a force F equal to pressure times the piston area, F = P × A. If the piston moves a small distance dx, the infinitesimal work is dW = F dx = P A dx. For a finite movement x at constant pressure, W = P A x. Since the change in volume is ΔV = A x, this is equivalent to W = P ΔV, and in general W = ∫ P dV when pressure varies. So the expression that matches this setup is pressure times piston area times the displacement, because it directly multiplies the pressure (the driving force per unit area) by the area to get force and by the distance the piston travels to get work. The units also work out to joules: Pa × m^2 × m = N/m^2 × m^2 × m = N·m = J. Other options don’t describe the work produced by the fluid on the piston in this context: density × height × velocity doesn’t yield the correct form or units for work; mass × gravity gives weight, not work; and while work is generally force × distance, that form doesn’t express the specific force from fluid pressure on the piston.