While deriving the energy equation for ideal fluid flow we took some assumptions, like, fluid is non-viscous and fluid flow is steady. But these assumptions stand true only for very specific cases. To deal with real fluid flows we have take into account different losses, called as head losses, caused by friction and sudden changes in flow path of the fluid. Moreover, the fluid flow was taken to be laminar in ideal case, but for real flow conditions fluid flows can be laminar as well as turbulent. Frictional losses for turbulent flows have relations, with flow parameters, different than laminar flow.
Modification to Energy Equation
For real flows we can keep the same energy equation, the Bernoulli Equation, but with some modifications. New modified equation should reflect two important aspects of real flows,
- Loss components
- Real velocity distribution
Loss term is appended to the equation and effect of real velocity distribution is taken into account by modifying the velocity term in the Bernoulli Equation.
Losses in Real Flow
Losses in real flow, actual it is the loss in energy associated with the fluid, are caused by resistances caused to the flow of fluid. Resistances are caused by two factors,
- Friction in Flow
- Change in flow path
Loss due to Friction in Flow
A part of energy of fluid while flowing is lost to the resistances due to friction caused by shear stresses. Shear stresses are different for laminar and turbulent flows; therefore, frictional resistances are also different.
For laminar flow shear stress is directly proportional to the viscosity and the velocity gradient along the section of fluid flow. As friction in a laminar flow is caused by shear stress, the frictional resistance or loss varies directly with the viscosity, the velocity and the length of the flow path.
For turbulent flow shear stresses are not directly proportional to the velocity. Shear stresses in turbulent flows do not have any defined analytical relation. For turbulent flows the relation of frictional resistances with the flow parameters are mainly empirical derived by dimensional analysis of experimental results. The frictional resistance in turbulent flow varies directly with the length of the flow path and square of the velocity of flow.
The frictional resistance in laminar flows doesn’t depend on the surface of the conduit through the flow occurs. But for the turbulent flows the frictional resistance also depends upon the roughness of the surface in contact to the flow.
Losses due to friction in flow are called as Major Losses, as they are responsible for a major part of energy loss. Losses due to change in flow path are called as Minor Losses. We will continue the derivation of energy equation for real fluid flows with Minor Losses in the next article.