Submitted by: Submitted by Fadzai
Views: 92
Words: 1666
Pages: 7
Category: Science and Technology
Date Submitted: 02/22/2014 02:26 AM
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...