Relationship of discharge and minor loss coefficient

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The discussion focuses on the relationship between the discharge coefficient (Cd) and the minor loss coefficient (k) in fluid dynamics, particularly regarding head loss (hl) and pressure drop (Δp). It references equations involving air density (ρ), pipe cross-sectional area (A), air velocity (u), and mass flow (m). The validity of the equations is supported by external sources, including a Neutrium article and Wikipedia. A specific concern is raised about the implications when the minor loss coefficient (k) is less than or equal to 1, questioning the complexity of this scenario. Overall, the relationship between these coefficients is crucial for understanding fluid flow in systems.
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What is relationship between discharge coefficient and minor loss coefficient. Am I right with that equations?
Mechanika_p_yn_w.png

hl – minor head loss
k – minor loss coefficient
ρ – air density
A – pipe cross section area
Cd – discharge coefficient
Δp – pressure drop
u – air velocity
m – mass flow

here is written that it is true:
https://neutrium.net/fluid_flow/discharge-coefficient-for-nozzles-and-orifices/
https://en.wikipedia.org/wiki/Discharge_coefficient

but what with case when k <= 1 ?
 
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is that question too difficult?
 
My idea is that I want to use immerse Whitetail Antlers in a fishtank to measure their volumetric displacement (the Boone and Crockett system is the current record measurement standard to place in a juxtaposition with) I would use some sight glass plumbed into the side of the tank to get the change in height so that I can multiply by the tank cross-section. Simple Idea. But... Is there a simple mechanical way to amplify the height in the sight glass to increase measurement precision...

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