Experiment 1 - Skin Friction PDF

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KRSPamintuanVirtual Experiment # 1Skin FrictionTheoryFluids flowing inside conduits experience resistance to flow not only due to their viscosity but also due to the conduit itself. The contact point between the fluid and the walls of the conduit introduces a type of friction called skin friction , ...

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Virtual Experiment # 1

Skin Friction Theory Fluids flowing inside conduits experience resistance to flow not only due to their viscosity but also due to the conduit itself. The contact point between the fluid and the walls of the conduit introduces a type of friction called skin friction, while disturbances within the flow such as obstructions, sudden turns, and sudden expansions and contractions in flow area are responsible for form friction. The friction in flow generally increases the energy needed to transport a fluid across the length of the pipe. Skin friction arises from the shearing force exerted by the solid boundary onto the flowing liquid. The larger the surface area of contact, the larger the effect of skin friction would be. The energy needed to overcome the total friction F for a fluid flowing inside a conduit is expressed as: 𝑢 2 4𝑓𝐿 (1) ( + 𝐾𝑓 + 𝐾𝑒 + 𝐾𝑐 ) 2𝑔𝑐 𝐷 where 𝑢 is the average velocity of the fluid, 𝑓 is the Fanning friction factor, 𝐿 is the total straight length of the pipe, 𝐷 is the internal diameter of the pipe, 𝐾𝑓 is the coefficient of form friction, while 𝐾𝑒 and 𝐾𝑐 are coefficients of friction for sudden expansion and contraction, respectively. 𝐹=

The contribution of skin friction to the total friction is the term collection of parameters that, when multiplied with

𝑢2 , 2𝑔𝑐

4𝑓𝐿 𝐷

. This is a dimensionless

will give the energy needed to overcome

skin friction. The term is dependent on the value of the Fanning friction factor f, which can be determined from correlations or graphs. 𝑓 is a function of Reynolds number and pipe smoothness, but theoretically is defined as: 𝑓=

𝜏𝑤

1 2 (2) 2 𝜌𝑢 where 𝜏𝑤 is the shear stress at the wall of the pipe, 𝜌 is the fluid density and 𝑢 is the bulk fluid velocity. For laminar flow in smooth tubes, the Fanning friction factor is determined from the Hagen-Poiseuille equation (equation 3): 16 𝑅𝑒 For turbulent flow through smooth pipes, the Blasius equation (equation 4) is used. 𝑓=

(3)

0.079 (4) 𝑅𝑒 0.25 If surface roughness is relevant in calculations, such as for very long pipes, a parameter called relative roughness (𝜖/𝐷) is included. The Churchill equation (equation 5) is used for such purposes: 𝑓=

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1

(5) 7 0.9 𝜖 = −4 log [0.27 + ( ) ] 𝐷 𝑅𝑒 The energy loss from skin√𝑓 friction can be related to the pressure drop through a length of pipe from the mechanical energy balance for incompressible flow:

Objectives • •

𝑢 2 4𝑓𝐿 −∆𝑃 ( ) = 2𝑔𝑐 𝐷 𝜌

(6)

To compute for the Fanning friction factor for a fluid flowing inside a pipe To determine the pressure drop of a fluid flowing inside of a pipe due to skin friction

Precautions Make sure to take rests in between activities while facing your computer to avoid eye and mind strain. Also, stay hydrated!

Procedure A. Familiarization with the simulator 1. Go to the simulator for the experiment: http://uorepc-nitk.vlabs.ac.in/exp1/index.html# 2. In the Simulator, play with the experimental set-up to be familiar with the flow of the fluid through the set-up. You simply set the parameters in the Set-up tab, then go to the Experiment tab and press the green button to pump the water, and rotate the main valve counterclockwise to let the fluid flow through the pipe and fittings. B. Determination of the Fanning friction factor 1. In the set-up tab of the simulator, set the parameters as follows: a. Length of pipe: 10 m b. Nominal diameter of pipe: 1 inch c. Process fluid: water d. Manometric fluid: carbon tetrachloride 2. Run the experiment and adjust the flow of water such that the rotameter reads 1 L/min. Record the height difference of the manometric fluid. 3. Determine the pressure drop of the fluid from the manometric reading. The pressure drop derived from the principles of fluid statics is: −∆𝑃 = (𝜌𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑙𝑢𝑖𝑑 − 𝜌𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑓𝑙𝑢𝑖𝑑 )𝑔∆ℎ 4. From the rotameter reading (volumetric flow rate), determine the average velocity of the process fluid. Remember that the volumetric flow rate is the product of the average velocity and the cross-sectional area of the pipe. The actual pipe diameter is given on the Experimental Data section (lower part of the simulator). 5. Calculate the Fanning friction factor from equation 6. Make sure that you take note of the actual pipe diameter given in the Experimental Data section. Label this as the observed friction factor. Note: for the properties of water, use the actual properties for water at 25oC. Use your handbook for the determination of physical properties. 6. Determine the Reynold’s number. Again, use the actual properties of water at 25oC. KRSPamintuan September 2020

7. Assuming that the pipe is smooth, determine the value of the friction factor by using either equation 3 or 4. 8. Determine the % difference of the observed and calculated friction factors. 9. Assuming that the pipe is rough, determine the value of the friction factor by using equation 5. The pipes are commercial steel pipes (∈= 0.0457 𝑚𝑚). 10. Change the rotameter reading three more times (evenly space it out before the manometric fluid spills out) and determine the corresponding friction factors and percent difference. 11. Play with the simulator! Change your manometric and process fluid to explore higher flow rates. Since mercury is so much denser than carbon tetrachloride, you can greatly increase the flow rate without spilling the manometric fluid. This is a great way to truly determine the effect of flow rate on pressure drop. You can also change your pipe length and diameter. 12. Develop graphs of your observations. The main graph worth noting is the pressure drop versus flow rate. You will have a better graph if you include more points, so don’t be limited by the procedure above. Another graph to consider is the friction factor versus Reynold’s number. 13. To make calculations easier, you may develop an Excel spreadsheet that utilizes the input values from the simulator and releases the desired computational values.

Guide Questions These questions could help you with the content of your lab report. 1. What is the effect of flow rate on the pressure drop? 2. What is the effect of the Reynolds number on the friction factor? 3. What do you think are the advantages and disadvantages of using different manometric fluids of differing densities? 4. Are the friction factors computed from smooth and rough assumptions very different? Why do you think this is the case?

KRSPamintuan September 2020

Experiment # 1

Skin Friction Final Data Sheet

Student’s Name

Instructor’s Signature

Course/Section

Date of Submission

A. Determination of friction factor Type of liquid: water Temperature: 25oC Manometric fluid: Carbon tetrachloride Length of pipe: 10 m Pipe internal diameter: 2.66 cm Fluid density: Fluid viscosity: Parameters

Run 1

Run 2

Run 3

Run 4

Rotameter reading, 𝑄 (L/min)

1

2

4

6

Average velocity, u (m/s) Manometric reading, ∆ℎ (cm) Pressure drop, −∆𝑃 (Pa)

Observed friction factor, 𝑓𝑜𝑏𝑠 Reynolds number Calculated friction factor assuming smooth pipes, 𝑓𝑐𝑎𝑙𝑐,𝑠𝑚𝑜𝑜𝑡ℎ Calculated friction factor assuming rough pipes, 𝑓𝑐𝑎𝑙𝑐,𝑟𝑜𝑢𝑔ℎ

% difference between observed and smooth friction factor % difference between observed and rough friction factor KRSPamintuan September 2020

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