- #1
Soumalya
- 183
- 2
Considering horizontal flow in a pipe (under the action of pressure forces only) if we focus on a fluid element we have a pressure gradient across the same i.e, a net pressure force will always act over the element that essentially maintains the flow.Now, in a region in the flow field if the specific volume of the fluid is 'v' and the average pressure immediately upstream (in excess of the downstream pressure) of a fluid element (of unit mass) considered in the region is 'p' then the work done by the resultant pressure force to push this element across a cross section is pv which is what is known as the 'flow work' or sometimes 'flow energy'.
Now, considering the fluid element again a net pressure force is always acting on it (as a result of the pressure gradient) and hence it should either accelerate or decelerate during the flow.This acceleration or deceleration is basically due to the net pressure force which is constantly doing work on the fluid element.According to the work energy principle of dynamics,the work done on the fluid element should result in an increase or decrease in the kinetic energy of the element.Thus, the kinetic energy of the fluid element seems to be a manifestation of the flow work being done on the fluid element.
Then my question is, why do we consider 'flow work' or 'flow energy' and kinetic energy of a fluid as separate quantities in the conservation of energy principle for fluid flow i.e, the Bernoulli equation?
The kinetic energy of the fluid seems to be a result of the work done by pressure forces in accordance with the work energy principle.For eliminating confusion one may also consider the flow of incompressible fluids whose specific volume is practically constant during the flow and hence a fluid element could be treated as a rigid body.
Now, considering the fluid element again a net pressure force is always acting on it (as a result of the pressure gradient) and hence it should either accelerate or decelerate during the flow.This acceleration or deceleration is basically due to the net pressure force which is constantly doing work on the fluid element.According to the work energy principle of dynamics,the work done on the fluid element should result in an increase or decrease in the kinetic energy of the element.Thus, the kinetic energy of the fluid element seems to be a manifestation of the flow work being done on the fluid element.
Then my question is, why do we consider 'flow work' or 'flow energy' and kinetic energy of a fluid as separate quantities in the conservation of energy principle for fluid flow i.e, the Bernoulli equation?
The kinetic energy of the fluid seems to be a result of the work done by pressure forces in accordance with the work energy principle.For eliminating confusion one may also consider the flow of incompressible fluids whose specific volume is practically constant during the flow and hence a fluid element could be treated as a rigid body.