Equations related to Bernoulli's equation?

In summary, the conversation discussed the engineering of a soap-dispensing shower head. The product will have a canister of soap on top of a basic shower head, separated by a mesh to control the flow of soap based on the water flow. The main mechanism for this is viscosity, but the question was raised about using equations to predict the amount of soap incorporated into the water. It was noted that the Bernoulli equation may not be accurate, as it is based on an inviscid fluid.
  • #1
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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  • #2
You mentioned that the main mechanism is viscosity, while the Bernoulli equation is based on an inviscid fluid. Thoughts?
 

Related to Equations related to Bernoulli's equation?

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid in motion. It is based on the principle of conservation of energy and is often used to describe the behavior of fluids in various systems.

2. How is Bernoulli's equation derived?

Bernoulli's equation is derived from the principle of conservation of energy, which states that the total energy of a system remains constant. In the case of a fluid, this means that the sum of the potential energy, kinetic energy, and internal energy remains constant. By equating the initial and final energies of a fluid in motion, Bernoulli's equation can be derived.

3. What are the assumptions made in Bernoulli's equation?

Bernoulli's equation is based on a number of assumptions, including the fluid being incompressible, inviscid, and steady state. It also assumes that the fluid is flowing along a streamline, there is no energy loss due to friction, and there are no external forces acting on the fluid.

4. How is Bernoulli's equation applied in real-life situations?

Bernoulli's equation is used to study and analyze various phenomena in fluid dynamics, such as the flow of water in pipes, the lift of an airplane wing, and the behavior of fluids in pumps and turbines. It is also used in fields such as meteorology, aerodynamics, and hydrodynamics.

5. Are there any limitations to Bernoulli's equation?

While Bernoulli's equation is a powerful tool in fluid dynamics, it does have its limitations. It is only applicable to ideal fluids and cannot account for factors such as turbulence, compressibility, and viscosity. In certain situations, other equations or models may need to be used in conjunction with Bernoulli's equation to accurately describe the behavior of fluids.

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