Good Report On The Bernoulli Equation

Abstract:

The understanding of the fluid flow characteristics is best achieved through the Bernoulli’s equation. It is the mathematical statement that relates the characteristics of the fluid and predicts fluid flow behaviors. Fluid flow behaviors differ in different conditions. In an ideal flow, taking the fluid as incompressible, non-viscous, and steady flow, the general formula for Bernoulli’s equation can be used where the Potential Energy, Kinetic Energy, and fluid pressures are accounted for. In other cases, the Bernoulli’s principle can be used to derive the mathematical formulas that best describe the conditions of the fluids and the environment where it is moving.
This activity studies the flow of fluids along venturi meters and orifice apparatus. The behaviors of the fluid flowing along the different environments are calculated using the Bernoulli’s principle. The various parameters that are needed for the computation can be found in the set-up such as the monometers for pressure readings, cross sectional areas of the inlet and the outlet, the valve for flow rate adjustment, and the heights of the pipes. In an orifice set-up, the fluids are moving from a fluid reservoir and discharged through nozzles. The parameters to understand the behaviors of the fluid can be derived and measured from the set-up such as the inlet and outlet diameter, flow rate adjuster, and the difference in the height of fluid before and after the movement. The differences in the fluid behaviors are explained through the Bernoulli’s equation. The Bernoulli’s principle can be used to predict the behaviors of fluid at certain conditions.
Key Terms:
Bernoulli’s Effect – it is the phenomenon described in the Bernoulli’s equation where the fluid flow velocity increase results to pressure decrease.
Ideal fluid flow – The fluid flow considered for general calculation with the assumption that there are no shear forces attributed to viscosity involved.

Fluid Pressure - It is defined as the normal force of the fluid exerted on a surface per unit area.

Venturi Meters – They are devices where fluids pass through a pipe stream with various diameters. Significant pressures are measured at the throat of the apparatus where the diameter is at the least.
Orifice – Apparatus with orifice consists of flat plate orifice with holes in it. Pressure in the upstream and the downstream as they pass through the tiny holes differ.

Introduction:

The Bernoulli Equation is a concise mathematical statement for the principles of conservation of energy for flowing fluids. The applicability of the second law of Newton which states that: F= ma, is used along the streamline of the continuous fluid. The “Bernoulli Effect” that occurs in flowing fluids is described in this equation. There is a lowering of the pressure of the fluid in certain regions when velocity is increased. In fluids with incompressible, non-viscous, and steady flowing characteristics, Bernoulli’s equation is stated as:

The equation is divided into three aspects:

The pressure energy = P1
The Kinetic Energy = ½ ρ v12; where ρ is the density of the fluid
Potential Energy = ρgh1; where h is the point of elevation from the reference
The Bernoulli equation is the equation that shows the reduction of the pressure during increase of fluid speed. The speed of the fluid is greatly affected by the streamline and the pathway. In an ideal fluid, the increase in the speed of the flow of fluids results to pressure decrease.
The fluid flow characteristics along various apparatus such as the venturi meter and orifice can be calculated using the Bernoulli’s equation. Venturi meters have pipe structures with gradual contraction. Orifice is another apparatus where fluid is discharged through a nozzle.