CVE 3033 : Luminous Intensity - Principles of Dimensional Analysis - Norris Model’s Discharging Rate - Engineering Assignment Help

Assignment Task :

OBJECTIVES

1. Apply the principles of dimensional analysis and similitude to a scaled – down model of Norris dam.

2. Analyze the flow rate across the dam.

3. Compare the actual flow rates with the Norris model’s discharging rate.

INTRODUCTION

Dimensional Analysis

An important tool in engineering is dimensional analysis. In its broadest definition, dimensional analysis is simply the comparison and manipulation of the dimensions or units of a quantity. There is a distinction between dimensions and units as follows:

• A unit is a precisely specified quantity in terms of which the magnitudes of other quantities of the same kind can be stated.

• Dimensions are quantities. In science, there are seven fundamental dimensions from which all other dimensions are derived.

Dimensional Analysis is very useful in checking calculations by ensuring that all the units in the intermediate steps cancel out to give the correct units of the final answer.

Similitude

Another tool available to engineers is the method of similitude. This method allows one to scale down or scale up any quantity as long as the units are preserved. Often in the engineering field, the actual size of an engineering prototype is very large, such as a dam, or very small, such as an integrated circuit. Working at the prototype scale then becomes extremely cumbersome. By using the method of similitude, it is possible to produce a scaled model in order to conduct laboratory experiments. In civil engineering, the prototypes are usually scaled down. The results of these experiments can then be scaled back up to the prototype’s scale to represent the characteristics of the prototype. In many cases, this reduces costs because prototypes are often very expensive to fabricate and test.

APPARATUS

The water channel will generate flow in the tank. A model of the Norris dam will be used to regulate this flow. The dimensions of the prototype and model of a Norris dam are as follows:

The scale for the above model is then 0.5 ft. to 100ft. or 1:200.

THEORY

Rayleigh Method of Dimensional Analysis

One method of dimensional analysis is the Rayleigh method. The Buckingham π (Pi) theorem is a key theorem in dimensional analysis and it is a formalization of Rayleigh’s method of dimensional analysis. Rayleigh’s method proves useful when a small number of variables are involved. As the quantity [of variables] becomes extensive, it is useful to utilize the Bukingham π theorem as the Raleigh’s method then gets too drawn out. Since the flow rate or discharge is of import to this lab, Q, identification of the variables that Q depends on comes first:

Where, H = water surface to the top of the dam

w = width of the dam

g = gravitational acceleration

p = density (constant)

k = constant efficient

Similitude
By similitude, there are three different types of similarities that can be used to relate the model’s characteristics to those of the prototype. They are:

• Geometric
• Kinematic
• Dynamic

PROCEDURE

1. Adjust the slope indicator to the zero mark.

2. Ensure that all the dials are off.

3. Plug in the apparatus.

4. Level the apparatus.

5. Ensure that the tailgate is horizontal by adjusting the knob near the control panel.

6. Measure and record the height of the Norris dam model, hdam

7. Take the width of the Norris dam model, wdam

8. Place the dam in the channel, and attach with screws.

9. Open the small and large orifice knobs slightly.

10. Turn on the pump.

11. Close the large orifice knob. 

12. Slowly open the small orifice knob to create the largest possible head difference on the manometers.

13. Record the value of this head difference.

14. Use the value of the head difference found in step 12 to determine the corresponding flow over the model, Qm, from the chart on the apparatus. Record this value.

15. Using a ruler, measure the height (Hupstream) of the water as it goes over the dam.

16. Close the small orifice slightly in order to decrease the head difference on the manometers.

17. Repeat steps 12 through 16 until 5 corresponding values of Qm and Hupstream have been obtained.

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