In this report I will use a pitot-static tube and a Venturi meter set up within an air flow rig to demonstrate the application of Bernoulli’s Equation and the assumption of inviscid flow. The air flow rig was set up and an imaginary matrix was defined across the cross sectional area of the air flow at the pitot-static section. The matrix had 4 cells going across (A, B, C, and D) the width and 5 cells down the height of the rig (1, 2, 3, 4 and 5). The pitot-static tube will be moved around to the centre of each cell so we can then take a reading for the pressure at that particular point, which can then be used to calculate the velocity across the matrix. This will enable me to determine how the pressure and flow performs in a non ideal situation by comparing the assumed volumetric flow rate at the pitot-static section with the calculated volumetric flow rate at the venturi. This will allow me to further discuss issues relating to why the values are different if they give different results. Theory
Bernoulli’s equations are based on ideal flows, this means the gases in question obey the equation of state; Pressure x Volume = Constant, and also suggests the flow has zero drag. In most cases flow does have some form of friction, either due to the viscous nature of the fluid or due to the turbulent behaviour of the flow (Sherwin & Horsley, 1996). The continuity equation is a form of the conservation of mass, applied to flowing fluids. In the flow the mass flow rate of the fluid entering and leaving the system must be the same (Sherwin & Horsley, 1996). It states the product of the density, area and velocity of a fluid is a constant in each particular case: ρ1A1v1=ρ2A2v2
Bernoulli’s energy equation is the conservation of energy applied to fluids and is shown as the following: P1ρ+v122+z1g=P2ρ+v222+z2g
This shows that the sum of the specific flow energy, the specific kinetic energy and the specific potential energy is a constant in a steady system. A steady system, however, assumes the following characteristics: * The flow has zero friction;
* The fluid is incompressible;
* There is no heat transfer;
* There is no work being done on, or by, the system.
We can multiply through by density to give a total pressure equation of the system at any particular cross section of the flow. It includes the static pressure - the potential pressure exerted in all directions by a fluid, the dynamic pressure - the difference in pressure levels from static pressure to stagnation pressure caused by an increase in velocity, and the hydrostatic pressure - the pressure which is exerted on a portion of a column of fluid as a result of the weight of the fluid above it: total pressure=P+ρv22+pzg
For systems that cohere to the assumptions above, the total pressure for any situation where the flow area takes a steady change is constant (Sherwin & Horsley, 1996).
A pitot tube is a velocity measuring device based on utilizing a pressure difference in a flow. It is a tube with an open end pointing into the direction of the flow and connected to a form of pressure measuring device, in the case of this investigation manometer using water. The equation for finding the velocity from the pitot-static tube for an incompressible flow is: v=2(P1-P)ρ
Where P1-P is the difference between the static pressure and the total pressure. (Bentley, 2005) The other type of device used is a venturi meter; this works on the principle of reducing the cross section of the flow so that there is a measurable pressure difference. There will be a measuring device incorporated into the pipe, with one end in the throat and the other in the wider cross section of the pipe, this measures the pressure difference. We can link this pressure difference in the following equation for volumetric flow rate: Q=A1v1=cdA22(P1-P2)ρ1-A2A1
This equation includes the coefficient of discharge, which is...