Where Does the 0.6 Constant in Torricelli's Equation Come From?

In summary, the general formula for Torricelli's equation is dH/dt*A(h)=-0.6*B*squareroot(2*g*h), where the constant 0.6 takes into account the effects of viscosity and turbulence. This value can be found using the discharge coefficient, which is influenced by the Reynold's number and the shape of the orifice.
  • #1
sting10
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Homework Statement



Hey, I am doing some work with torricellis equation and I have some questions. I am using the equation:

dH/dt*A(h)=-B*squareroot(2*g*h)

My question is, in my textbook it says the general formula is:

dH/dt*A(h)=-0.6*B*squareroot(2*g*h)

I want to know where the constant 0.6 comes from. Is it a constant which takes height for viscosity or turbulence and if so how do I find this constant?

Thanks.
 
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Welcome to PF!

Hi sting10! Welcome to PF! :smile:

(have a square-root: √ :wink:)
sting10 said:
… I want to know where the constant 0.6 comes from. Is it a constant which takes height for viscosity or turbulence and if so how do I find this constant?

From http://en.wikipedia.org/wiki/Bernoulli's_principle#Real_world_application" …
The maximum possible drain rate for a tank with a hole or tap at the base can be calculated directly from Bernoulli's equation, and is found to be proportional to the square root of the height of the fluid in the tank. This is Torricelli's law, showing that Torricelli's law is compatible with Bernoulli's principle. Viscosity lowers this drain rate. This is reflected in the discharge coefficient which is a function of the Reynold's number and the shape of the orifice.[23: Mechanical Engineering Reference Manual Ninth Edition]
 
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FAQ: Where Does the 0.6 Constant in Torricelli's Equation Come From?

What is Torricelli's law?

Torricelli's law, also known as Torricelli's theorem, states that the velocity of a fluid escaping from a small opening near the bottom of a container is equal to the square root of 2 times the acceleration due to gravity (g) times the height of the fluid above the opening (h). It is named after Italian physicist Evangelista Torricelli who first discovered this principle in the 17th century.

How is Torricelli's law related to viscosity?

Torricelli's law is closely related to viscosity, which is a measure of a fluid's resistance to flow. In simple terms, the greater the viscosity of a fluid, the slower it will flow through an opening, and the smaller the velocity will be according to Torricelli's law. This is because higher viscosity fluids have stronger internal forces that resist the flow, resulting in a lower velocity.

What factors can affect the accuracy of Torricelli's law?

There are several factors that can affect the accuracy of Torricelli's law, including the shape and size of the container, the type and temperature of the fluid, and any external forces acting on the fluid (such as air pressure). Additionally, Torricelli's law assumes that the fluid is incompressible and that there is no turbulence in the flow, which may not always be the case.

How is Torricelli's law used in real-world applications?

Torricelli's law has numerous applications in various fields, such as hydraulics, aerodynamics, and fluid mechanics. It is commonly used to calculate the flow rate of fluids through pipes and nozzles, as well as to design and optimize the performance of pumps, turbines, and other fluid-based systems. It is also used in weather forecasting to measure air pressure and predict changes in atmospheric conditions.

Can Torricelli's law be applied to all types of fluids?

Torricelli's law is most accurate for incompressible fluids, such as water and oil, which have constant densities and do not change significantly under pressure. It can also be applied to gases, but only under certain conditions, such as when the gas is flowing slowly and the temperature remains constant. For highly compressible fluids, such as air, other equations and principles must be used to accurately calculate the velocity of flow.

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