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I am writing to ask for help with a T-junction pipe problem. Attached picture shows the pipe configuration. The schematic shows a large pipe with ID 16.5mm and smaller 4mm ID tubes connected to it. The insertion has an extruded bit of tube there. The flow inlet is on the left and outlet on the right, the smaller tubes are connected to emitters, where the flow rate out of the emitters depends on the local inlet pressure.

I am using the Darcy-Weisbach eqn to model the frictional head loss and a modified version of Darcy-Weisbach eqn to model the elastic tube head loss, the insertion head loss is modelled with a minor head loss eqn.

I want to model the flow rate and head of this pipe section. From what I know so far, the head losses in this system are frictional head loss along straight pipe sections, head loss due to tube insertion and a head loss along the smaller elastic tube. To calculate the local pressure at the emitter inlet, the inlet head should be deducted by all 3 components of head loss mentioned.

My question is, for pressure inside the large pipe, specifically at line 0 in the diagram, do I need to include the head loss due to the elastic pipe? Or in better representation, is the equation below accurate?

$$H_{in} - (H_{fric} + H_{insertion} + H_{elastic}) = H_0$$

Pipe line with tubes connected

Edit 20/11/2020:

I did some research on fluid mechanics, which leads to me to the Euler's equation along a streamline. Integrating that eqn yields the Bernoulli's eqn or the energy equation, which is the equation that I am modelling the pipe pressure with.

$$ \frac{dH}{dL} = \frac{z}{dL} + \frac{dh}{dL} + {\frac{d(\frac{v^2}{2g})}{dL} } $$ Ignoring the dynamic pressure term and no change in elevation, $$H_{in} - (h_{fric} + h_{insertion}) = H_0$$

If the Bernoulli's eqn is a streamline equation that describes the pressure of the fluid flow along the streamline, and these assumptions have to be made:

  1. Incompressible and inviscid fluid flow
  2. Steady state flow
  3. Irrotational flow
  4. Uni-directional flow

From what I understand, this equation then should not be applicable in T junction flows, as the flow is no longer uni-directional and this equation can no longer model the entire flow area.

However, I computed the pressure of a T junction flow problem with this equation then compared with empirical data and it matches to an acceptable accuracy, why is it so?

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The head at point 0 will be: $$H_0 = H_{in} - (H_{fric}+H_{insertion})$$

The head lost from the plastic tubing does not impact the inlet conditions.

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  • $\begingroup$ Hi, thanks for your response :), Just to clarify, the head loss at pipe section 0 is affected only by the frictional head loss and the tube insertion head loss, and the only effect on the subsequent section's (section 1) pressure is the flow out of the tubing. Is that accurate? $\endgroup$
    – Limpeh
    Commented Oct 6, 2020 at 8:37
  • $\begingroup$ After point 0, the pressure loss to point 1 is the same exercise as what was done from the inlet to point 0 but you need to run the calculations for when there is flow out of the first user and when there is no flow out of the first user. $\endgroup$
    – J. Ari
    Commented Oct 6, 2020 at 18:59

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