14.12 : 流体の定常的な流れ

Consider a control volume, such as a pipe with solid boundaries. As fluid flows within the pipe, it changes direction due to the impulse exerted by the resultant force from the pipe walls.

In steady flow, the amount of fluid with mass dm entering the control volume at time t, with velocity v₁, is equal to the amount leaving the control volume at time t + dt, with velocity v₂.

The momentum of the fluid within the control volume remains constant during the time interval dt.

Applying the principles of linear and angular impulse and momentum, and dividing both equations by dt, yields the resultant external force and moment about an arbitrary origin point O, respectively.

The term dm/dt is the mass flow, which indicates the constant inflow and outflow of fluid per unit of time.

Generally, the mass flow is expressed as the product of the density of the incompressible fluid and its discharge flow.

The discharge flow, also known as the volumetric flow, measures the volume of fluid flow per unit of time.