1. Acceleration and Bends

2. Acceleration length and Associated Friction
When the solids enter into the piping system or when a flow direction is changed such as through a bend, there is a certain distance traversed by the solids before they re-establish a steady state. Generally in this acceleration or re-acceleration distance the friction and thus the pressure drop loss is different that in the steady state flow. A couple of expressions to addressed this phenomena are presented.

3. Acceleration Length Acceleration Length Quick Approximation for Acceleration Pressure Drop

4. Bend Analysis
As mentioned previously, horizontal and vertical flows are not always possible in pneumatic conveying. The flow must traverse bends. Usually two contributions are assumed with a linear effect, the gas only energy loss across a bend and a solids flow contribution. Ito did one of the most comprehensive studies on gas only energy loss and is presented below.

5. Bend Analysis – gas only
Ito – single phase flow
RB – radius of the bend
R0 – radius of the tube
L – length of the bend
0.034<Re(r0/RB)2<300
Below one can use straight tube analysis

6. Schuchart Bend Analysis