# EN400 LAB #2 PRELAB. ARCHIMEDES & CENTER of FLOTATION

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1 EN400 LAB #2 PRELAB ARCHIMEDES & CENTER of FLOTATION Instructions: 1. The prelab covers theories that will be examined experimentally in this lab. 2. The prelab is to be completed and handed in to your instructor at the beginning of the lab period. 3. If you can, answer the questions without referring to your notes. Only refer to your notes if you are confused or fail to understand a concept. This will greatly improve your understanding of the concepts this lab is designed to reinforce. 4. By conscientiously completing this prelab, you will have a thorough understanding of what the lab is trying to show. Your lab performance will be maximized. 5. For full credit, all work must be shown. Show generalized equations, substitution of numbers, units, and final answers. Engineering is communication. Work that is neat and shows logical progression is much easier to grade. Student Information Name(s): Section: Date: PRE-LAB 2-1

2 Lab Apparatus In this lab, two simple wooden hull shapes are used as floating bodies (one symmetrical shape and one unsymmetrical shape). Their tops have been inscribed so that half-breadths can be measured and used to determine hull form characteristics. At the bow and stern are draft marks measured from the keel. The tank in which they will float has been fitted with a weir and a spillway through which any displaced water will run and be collected for measurement. This opening, in effect, provides a constant water level in the tank. A suitable container for collecting the water, a scale for weighing the hull shape and displaced water, and a ruler for taking measurements are provided. Theory Archimedes Principle and Static Equilibrium In the first part of the lab, the displacement (weight) of the symmetrical hull will be determined by three different means: Weigh the model hull on a scale The volume of water it displaces will be weighed on a scale Its underwater volume will be calculated and used to calculate buoyant force and displacement 1. Which of the techniques described above will give the most accurate weight? Why? 2. Which of the techniques described above could be applied to a full-sized ship? Why? Archimedes Principle states that: An object partially or fully submerged in a fluid will experience a resultant vertical force equal in magnitude to the weight of the volume of fluid displaced by the object. This vertical force is called the force of buoyancy and it is given the symbol FB. 3. Write the mathematical relationship described by Archimedes Principle that links FB with the submerged volume ( ) of a floating body. PRE-LAB 2-2

3 4. When placing the wooden models in the tank of water, if they float (positively buoyant) will they be in static equilibrium? 5. What are the two necessary conditions for an object to be in static equilibrium? Condition 1: Condition 2: 6. Using the conditions for static equilibrium, write the mathematical relationship that links the buoyant force (FB) being experienced by a floating body and its weight or displacement ( ). 7. Combine the expressions given in (3) and (6) to give the mathematical relationship linking the submerged volume of a floating object ( ) with its displacement ( ). 8. On the section of a floating hull form below, draw the two force vectors described above, and clearly show and name the centroids through which they act. C L WL B 9. Describe how the positions of the two centroids displayed above are located on a ship, by filling in the table below. Vertically Referenced From Acronym Name Transversely Longitudinally PRE-LAB 2-3

4 Center of Flotation Theory 10. On the three orthogonal views of a hull form below, draw in the waterline, centerline, midships, and show the center of flotation on EACH view. 11. What is the significance of the center of flotation with regard to the waterplane? 12. Describe parallel sinkage: 13. Where would a weight have to be placed on a ship to achieve parallel sinkage? 14. Complete the table below to describe how the center of flotation is referenced on a ship. Transversely Longitudinally Referenced From Acronym Name PRE-LAB 2-4

5 EN400 LAB #2 ARCHIMEDES & CENTER of FLOTATION Instructions: 1. This lab is conducted in the Hydromechanics Lab on the ground floor of Rickover Hall. 2. Prior to arriving, read through the lab procedure so that you are familiar with the steps necessary to complete the lab. 3. Bring this handout and a calculator to the lab. 4. The lab is to be performed in small groups of 2 or 3. Your instructor will specify whether the group or each individual must submit the completed lab. 5. Follow the stages of the lab in consecutive order. The lab follows a logical thought pattern and jumping ahead without completing the intervening theory questions will limit your understanding of the concepts covered. 6. For full credit, all work must be shown on the lab. Show generalized equations, substitution of numbers, units, and final answers. 7. Keep your workstation (including the floor) clean and dry. Ensure all equipment and the models are returned to their original location when you complete the lab. Student Information: Name(s): Section: Date: LAB 2-1

6 Part 1: Archimedes Principle and Determination of Displacement 1. Weigh the symmetrical model on the scale and record its weight below. Scale weight of symmetrical model (lb) This weight corresponds to the displacement ( ) of the model. The remainder of Part 1 of the lab verifies this weight using two different techniques. Displacement Measurement from Weight of Displaced Water Fill the tank to a level just above the height of the weir and let the excess water flow into a bucket. Allow about 5 minutes for the water to stop dripping. Empty the bucket into a sink or drain DO NOT DUMP EXCESS WATER INTO THE TOW TANK. Also ensure the small can is empty. 2. Weigh the empty bucket and record its weight in the table below. Holding the large bucket under the weir, carefully lower the model into the tank making sure you keep the model upright. After the initial rush of water, the remaining dripping water can be caught in the small can. Wait at least 5 minutes for the water to finish dripping over the weir. While you are waiting, complete steps (4) through (7). 3. Pour the water from the small can into the bucket and complete the table below. This table only requires data collected up to this point and application of course principles (Archimedes and Static Equilibrium) Weight of Empty Bucket (lb) Weight of Collected Water and Bucket (lb) Weight of Collected Water (lb) Based on data up to this point in the Lab, what values would you expect for: Magnitude of Buoyant Force, FB (lb) Displacement of Model, (lb) 4. Explain how you arrived at the value for the displacement of the model. LAB 2-2

7 5. The mean draft (TM) is the average of the forward and aft drafts as measured at their respective perpendiculars. Use this relationship and observations of the floating model to complete the table below. Taft (inches) Tfwd (inches) TM (inches) 6. Using your value for TM and assuming that the model is of uniform density, estimate the following values that describe the location of the centers of buoyancy (B) and gravity (G) for the floating symmetrical model. Note: Ignore the weight of the handles. The center of gravity of a homogenous object, such as the ship model, is the centroid of the volume of that entire model. Centroid Parameter Value (inches) Center of Buoyancy (B) KB (VCB) TCB LCB Center of Gravity (G) KG TCG LCG 7. Confirm your understanding of these quantities by plotting the location center of buoyancy (B) and the center of gravity (G) on the shear and body views of the symmetrical model below. Ensure you accurately locate these centroids relative to the waterline. WL B L O )( C L LAB 2-3

8 Displacement Measurement from Submerged Volume Calculation 8. In the space below, calculate the waterplane area of the symmetrical model using Simpson s first rule. For full credit, ensure you include the following steps: a. Draw a sketch of the area you are determining. b. Write the generalized equation for Simpson s first rule. c. Calculate waterplane area and box your answer. 9. Now determine the submerged volume ( ) of the model. Note: On the symmetrical model with vertical sides, we can calculate volume as we would a cylinder (area * height) LAB 2-4

9 10. Why can t this technique be used to calculate the submerged volume of a normal hull form? 11. Calculate the buoyant force from the value of submerged volume and the density of the water in the tank. 12. Now calculate the symmetrical model s displacement ( ). Analysis of Results 13. From the observations and calculations you have made, complete the following table. Calculate the percent error in that table cell, as compared to actual scale weight of model. Technique Displacement, (lb) Percent Error Explanation of Error Scale Weight of N/A N/A Model Scale Weight of Displaced Water Simpson s Rule 14. Explain how these values verify Archimedes Principle and the principle of static equilibrium? LAB 2-5

10 Part 2: Longitudinal Center of Flotation 15. Carefully place the non-symmetrical model in the tank and complete the table below. Unloaded Condition Taft (inches) Tfwd (inches) TM (inches) Trim (inches) 16. By observing the shape of the non-symmetrical model, qualitatively estimate the position of the center of flotation (F). Circle one of the answers below. Forward of midships At midships Aft of midships Making sure you have a can ready to collect any displaced water; carefully load the model on the centerline at Station 4 with a 5-pound weight. 17. Record the model s drafts in the table below. Loaded Condition Taft (inches) Tfwd (inches) TM (inches) Trim (inches) 18. Comparing data from the Unloaded and Loaded conditions, what change in trim (δtrim) has occurred? δtrim = Why has this occurred? 19. What is the name of the point where the weight would have to be placed on the model in order to achieve zero change in trim (δtrim = 0 inches)? 20. By a trial and error basis, move the 5-pound weight so that parallel sinkage is achieved. When you are satisfied, complete the following table. Loaded for δtrim = 0 Condition Taft (inches) Tfwd (inches) TM (inches) Trim (inches) LAB 2-6

11 21. Measure the location of the 5-pound weight to determine a value for the longitudinal center of flotation of the non-symmetrical hull. (Reference to amidships) LCF = 22. Using the data collected, calculate the Pounds Per Inch Immersion (PPI) of the nonsymmetrical model. 23. Using the collected data, calculate the model s Moment to Change Trim One Inch (MT1 ). Recall that δtrim = w * l / MT1, where w=weight, l=longitudinal distance. LAB 2-7

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