Experiment 1

INTRODUCTION

Learning Outcomes

To carry out various exercises that would help students describe the characteristics of fluid flow due to potential energy under constant and variable head conditions for an upright, cylindrical tank.

Theory

Bernoulli’s principle assumes that energy in incompressible, frictionless, ideal liquids is continuously being interconverted from one form to the other. The appropriate form of Bernoulli’s equation that sets the outlet as the datum height, assumes no work is done by the system, potential energy is converted to kinetic energy and ignores pressure energy is: (1) mgh=12mu2

Where:

m is mass

g is acceleration due to gravity

h is height above outlet

u is the discharge velocity

A is cross sectional area

Q is volumetric flow rate

Where:

m is mass

g is acceleration due to gravity

h is height above outlet

u is the discharge velocity

A is cross sectional area

Q is volumetric flow rate

This helps us derive the Torricelli equation used to find instantaneous discharge velocity at a particular height:

(2) u=2gh

This will then be compared to average discharge velocity, obtained by:

(3) u=Q/A

Then finally to find the dimensionless discharge coefficient:

(4) CD=uu

The equation relating height change with time is derived as follows. Since volumetric flow rate into and out of the tank is the same:

(5) QOrifice=QTank

Cd.AOrifice2gh=-ATank.dhdt

1h0.5 dh=- Cd.AOrifice2gATankdt

h t=(-Cd.AOrifice2gATank t+K)2

Relevance

Finding out how the discharge velocity changes under variable conditions allows engineers to make calculations or approximations regarding the residence time of materials in a vessel. This is especially important for reactive systems in which homogenous reactants need to mix well in order to achieve high yield. For continuous processes this means determining the optimum input and discharge velocity that the plant units...