The velocity does not have necessarily a plug profile at the inlet and outlet of a control volume and the cross sectional areas might also differ at the inlet and outlet of a CV. The variations in the cross sections of flow conduits and the velocity profiles have to be accounted to calculate the correct pressure drop due to the viscous losses. Therefore, the surface integrals has to be calculated by considering these variations:
The conversion of mechanical energy (A) and the irreversible conversion and loss of mechanical energy with viscous dissipation (B) can be better distinguished.
The total pressure drop consist of major losses, which are due to frictional effects
in fully developed flow in constant area tubes, and minor losses, which occur
at entrances, sudden area changes, bends, elbows, fittings, valves, contraction
and diffusers, etc..
For non circular ducts, which appears in air conditioning, heating and ventilating applications, an equivalent diameter is calculated so that correlations for circular pipes can be utilized.
This equivalent diameter is called as hydraulic diameter:
However, for the vast variety of geometries, it is not possible to obtain relations as for the pipe flows. Thus, $\zeta$ for each component is measured and documented.
A single pipe system may have many minor losses. Since all are correlated with $0.5\rho {\bar {U}}^{2}$, they can be summed into a single total system loss if the pipe has constant diameter:
The solution for pipe network problems
is often carried out by use of
node and loop equations similar in many ways to that done in electrical circuits.
The net flow into any junction must be zero.
The net head loss around any closed loop must be zero. At each junction there is one single pressure.
All head losses must satisfy the major and minor-loss friction correlations.
In such problems the pipes and components might have different areas, thus pressure loss at each pipe and component should be calculated separately. Moreover, there can be components with unknown properties.
For such cases it is found useful to formulate the pressure loss as a function of the flow rate:
The utilization of the explained concepts will be demonstrated in the class by developing an inhaler from scratch. The basic steps of the design are as follows:
Make a conceptual design
Decide pressure drop-flow rate characteristic of the inhaler (Inhaler patient matching)
Dimension each component of the inhaler to ensure
Pressure drop-flow rate characteristic
Full emptying of the blister
Sufficient dispersion of the powder composition
An overview of dry powder inhaler design could be found in in the following publication ^{[1]}
↑Int J Pharm. 2011 Sep 15;416(1):25-34. doi: 10.1016/j.ijpharm.2011.05.045. Epub 2011 Jun 28. A method for the aerodynamic design of dry powder inhalers. Ertunç O, Köksoy C, Wachtel H, Delgado A.