Torricelli s law

In the second case the outlet flow rate is given by Torricelli s Law, that is, qsoln=... 

Mechanism of Water Flow from Tank—Torricelli s Law... 

It turns out that bl is the square root of 2 g, where g is the acceleration due to gravity. Thus in full form Torricelli s law is ... 

Although Torricelli did not know this, his work helped to point Newton in the right direction. Therefore, Torricelli s Law is the constitutive relationship that we seek to complete our model. We return to that endeavor now. 

The mass flow term in can be taken as the product of the density of the fluid and its volume flow rate. The mass flow out can be specified by Torricelli s Law multiplied by the fluid density and the mass in the control volume is the product of the fluid density, the tank s cross-sectional area, and the level at any time t. This gives us the following equation ... 

In this expression Aoo is the nominal aperture size to deliver at the design flow rate based on the constant set input flow rate. The second term in the parenthetical expression is the product of a proportionality constant K and the difference between the set point level and the actual level as a function of time. We substitute this for Ao in Torricelli s Law and also in the equation describing a system with sinusoidally fluctuating input flow ... 

The solutions show two important aspects of this model as written The concentrations come to a constant and equal value and the volume continues to rise indefinitely. The reason for this is that we took the outlet concentration to be a constant. Although this may have made for a simple model to solve, it is also one that is not very realistic. The tank would be overflowing. A more realisitc model would be one in which the exit flowrate was either set to match the inlet flow rate, which would make zero and the volume a constant at its initial level, or we could assume the flow rate out was gravity driven and would respond to the level in the tank, that is, Torricelli s Law. 

Recall that pi is just the density of the pure liquid solvent, and that h[t] = can be replaced into Torricelli s Law. These equations have become complicated enough that we shall define the density upfront and let NDSolve handle the work of solving the simultaneous equations (see the In statement that follows) ... 

However, we will not make any of these simplifying assumptions. Instead, we will take the flow out as given by Torricelli s Law and the density of the solution to be a linear function of the salt concentration. Then all we need to do is to modify the numerical routine we had for the previous problem by eliminating the term for the salt feed ... 

This was one of the earliest rational laws of hydraulics (1643), known as Torricelli s theorem from its discoverer, who was a student of Galileo. According to the definitions just given, the actual velocity of the jet is... 

How Torricelli s invention measures the pressure of the atmosphere is explained by Newton s second law of motion, which states ... 

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