Torricellis Equation and Its Variants

The most interesting applications of Bernoulli s equation include the effects of friction. Before we can solve these, we must learn how to evaluate the term, which we do in Chap. 6. However, in many flow problems the friction heating terms are small compared with the other terms and can be neglected. We can solve these by means of Bernoulli s equation without the friction heating term. A good example of this type of problem is the tank-draining problem, which leads to Torricelli s equation. 

Example 5.2. The tank in Fig. 5.5 is full of water and open at the top. There is a hole near the bottom, the diameter of which is small compared with the diameter of the tank. What is the velocity of the flow out the hole  

To solve this i)roblem, we apply Eq. 5.7 between the free surface at the top of the tank, location 1, and the jet of fluid just after it has left the tank, location 2. In addition to the assumptions built into Bernoulli s equation, we assume the following  

The diameter of the tank is so large that the velocity at the free surface is practically zero] = 0. 

The pressures at locations 1 and 2 are the local atmospheric pressures. The pressure of the jatmosphere is not exactly the same at both points, but it is practically the same so we assume AP = 0, 

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