Basisvergelijking voor drukveld

Consider a small rectangular fluid element with the lengths of the edges assumed to be taken from any arbitrary location within the fluid mass of interest.

Two types of forces act on this element, including surface forces caused by pressure and a body force equal to the element's weight.

If the pressure is denoted at the center of the element as p, the average pressure on the different faces can then be described in terms of p and its derivatives.

To understand the effect of the forces on the fluid element, the resultant surface force in the y direction can be expressed, and similarly, for the x and z surfaces.

The resultant surface force acting on the element can now be represented in vector form and further expressed as the resultant surface force per unit volume.

The weight of the element can be expressed using the specific weight of the fluid.

Newton's second law for the fluid element can be expressed using the resultant surface force per unit volume and the element's weight.

With this, the equation of the pressure field can be obtained.