(III) In Fig. , take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is

where , and and are the areas of the opening and of the top surface, respectively. Assume so that the flow remains nearly steady and laminar.

FIGURE 10-54 Problems 48 and 49

Solution 48P:

We have to derive the equation of the velocity of water from the opening at the bottom of the container. This velocity of water is also known as velocity of efflux.

Step 1 of 4

Concept:

Continuity Principle: For the streamlined flow of water, the product of cross sectional area at any point to the velocity of water at that same point is always constant. Mathematically,

…(a)

Bernoulli’s Principle: The sum of the pressure energy, kinetic energy and potential energy for a streamlined system is always constant. Mathematically,

…(b)