STATIC FORCES ON SOLID BOUNDARIES

The force exerted on a solid boundary by a static pressure is given by 

Note that both force and area are vectors, whereas pressure is a scalar. Hence the directional character of the force is determined by the orientation of the surface on which the pressure acts. That is, the component of force acting in a given direction on a surface is the integral of the pressure over the projected component area of the surface, where the surface vector (normal to the surface component) is parallel to the direction of the force [recall that pressure is a negative isotropic stress and the outward normal to the (fluid) system boundary represents a positive area]. Also, from Newton s third law ( action equals reaction ), the force exerted on the fluid system boundary is of opposite sign to the force exerted by the system on the solid boundary. 

This relation determines the pipe wall thickness required to withstand a fluid pressure P in a pipe of radius R made of a material with a working stress a. 

The dimensionless pipe wall thickness (times 1000) is known as the Schedule number of the pipe  

This expression is only approximate, as it does not make any allowance for the effects of such things as pipe threads, corrosion, or wall damage. To compensate for these factors, an additional allowance is made for the wall thickness in the working definition of the schedule thickness, ts  

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