Equations related to Bernoulli's equation?

AI Thread Summary
The discussion focuses on applying Bernoulli's principle to predict soap incorporation in a shower head design. The user seeks equations to estimate the amount of soap mixed with water based on flow rates, emphasizing that viscosity plays a significant role. There is a recognition that Bernoulli's equation typically applies to inviscid fluids, raising questions about its applicability in this scenario. The need for a balance between viscosity effects and flow dynamics is highlighted. Accurate predictions are sought within a 20-25% margin of error.
DyslexicHobo
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I'm writing an engineering white paper on a soap-dispensing shower head. The product will have a canister of soap on top of a basic generic shower head separated by a mesh so that due to the viscosity of the soap, the flow of the water rushing by will be the main determining factor on how much soap comes through (rather than gravity pulling it at a constant rate). From what I have researched, the pulling of the soap into the water would be due to Bernoulli's principle.

I'm just wondering if there's any equations that I can use to accurately (within 20-25%, even) predict how much soap will be incorporated into the water at a given rate of flow for the water.
 
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You mentioned that the main mechanism is viscosity, while the Bernoulli equation is based on an inviscid fluid. Thoughts?
 

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