# Flow Measurement - Fluid Mechanics

**Topics:**Fluid dynamics, Orifice plate, Mass flow rate

**Pages:**7 (1800 words)

**Published:**April 16, 2013

Class: DME2

Title: Flow Measurement

Date: 11/02/2013

Lecturer: Mr Higgins

Summary:

In this experiment many different meters were used to measure fluid flow rate; the orifice plate, the venture meter, the rota meter and the weigh tank. Each meter works by its ability to alter a certain physical property of the flowing fluid and then allows this alteration to be measured. The measured alterations are linked directly to the flow rate and these measurements are subbed in to adjusted equations to solve for it. Each methods outcome is then analysed, compared against each other. 1. Objectives:

* To introduce the student to three typical methods of measuring he flow rate of an incompressible fluid namely; 1- Venturi metre

2- Orifice plate

3- Rotor metre

* To compare the accuracy of each device.

* To give insight into appropriate industrial application for each device.

2. Theory:

Water enters and first flows through the Venturi metre, then through the Orifice plate and then through the Rotor meter. On leaving the Rotor meter the water flows via a control valve to the weigh-tank of the hydraulic bench. At the inlet and the outlet of each flow measuring device is a connection to the manometer board, this allows the head loss to be determined across each device.

For an incompressible fluid flowing through a pipe the following equations apply: Continuity, Q=V1A1=V2A2(1)

Bernoulli’s P1ρg+V122g+z1=P2ρg+V222g+z2(2)

Venturi

Rewriting Bernoulli’s equation for the experimental apparatus PAρg+VA22g+zA=PBρg+VB22g+zB

Since apparatus is horizontal ZA=ZB therefore,

PAρg+VA22g=PBρg+VB22g

Rearranging

VB22g+VA22g=PAρg+PBρg

Since P/ρg is the hydrostatic (pressure) head, h at any given point we can rewrite the above equation as, VB22g+VA22g=hA-hB(3)

Where hAand hB are read directly from the apparatus.

To solve for velocities, we rearrange equation (1),

VA=VBABAA

Filling into equation (3),

VB22g+VBABAA22g=hA-hB(4)

Hence the only unknown asVB.

Therefore, to find the flow rate, determine VB from equation (4) and then Q is given by. Q=VBAB (5)

Orifice

Q is calculated using the same procedure as the Venturi meter using ports E and F as opposed to A and B. However, because the orifice plate is less ideal, it causes turbulence in the flow it requires a correction factor known as the coefficient of discharge, K. For this apparatus K=0.601 therefore, the calculated Q must be multiplied by K, Qactual=Qtheoretical×K

Rotor meter

The flow rate is read directly off the rotor meter calibration curve as seen in the graph h below.

3. Apparatus:

* The bulk of the apparatus used in this experiment is as shown below on a labelled diagram. * The flow of water was manually varied by a screw type tap. * The weight balance is not shown but is acted on a counter balancing weight system. In this experiment a 4kg weight was dropped and the time was started. The length of time was determined by how long it would take for the water to raise the weight. This (with a 1:3 weight is to water ratio) allowed the mass flow rate to be calculated.

Rotameter

Rotameter

Manometers

Manometers

4. Orifice

Orifice

Venturi

Venturi

Procedure:

1. Set flow rate to maximum.

2. Record the monometer readings A, B, E and F.

3. Measure the discharge using the weigh-tank.

4. Repeat the steps 2 and 3 for 6 other flow rates.

5. Draw a graph of volumetric flow rate measured by the weigh-tank versus volumetric flow rate measured by the other three devices (all on one graph). 6. Discuss the advantages and disadvantages of each device from an installation view.

5. Experimental Results:

| Amm| Bmm| Emm| Fmm| Rota-meter| Flow rate (weigh – tank) @4kg (s)| 1| 378| 131| 349| 86| 21.4| 25|

2| 345| 162| 326| 130| 18.4| 31.8|

3| 320| 188| 304| 165| 15.2| 37|

4| 298...

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