What are three ways to increase friction on wet or icy roads?
What are the three ways to increase friction on a wet or icy roads?
11.8.1 Soil Friction Factor. The friction factor is defined as the ratio between the force required to move a section of pipe and the vertical contact force applied by the pipe on the seabed. This simplified model (Coulomb) is used to assess stability and requires an estimate of the friction factor.
Does sand reduce friction?
No, sand does not reduce friction but increase friction. Read More
Is sand wet?
Why is wet sand darker than dry sand?
Why do sparks occur in wet sand when you stamp on it?
this may be possible do to mineral content within the grains of sand, stamping causes both compression and friction wich may cause energy to be released thus the sparks. Read More
Why is wet sand at the beach cooler to walk on than dry sand?
because wet sand is cold from the cold water that makes it wet, and dry sand is in the sun and the water cant reach all the sand. Read More
Why does dry sand weigh more than wet sand?
It doesn't - wet sand weighs more for the same volume than dry sand. Read More
Does sand paper reduce friction?
sand paper increases friction, that is to say that it is harder to slide something on sand paper than it is on a smooth surface. Read More
Which has less friction a dry road or a wet road?
A wet road has less friction since the water acts as a lubricant. Read More
![Friction Factor Of Sand Friction Factor Of Sand](/uploads/1/2/5/7/125729763/818689768.png)
What can happen to wet soil during the shaking from an earthquake?
liquefaction factor (sinking sand due to becoming like liquid) Read More
Why is sand wet?
This is a joke everyone. Why is sand wet? Answer: probably cuz theres water mixed with it. Read More
Is wet sand an element?
If a water slide was dry how would the friction be different?
Water can absorb friction because it's wet and slippery. When things are dry, there nothing slippery or wet to absorb the friction, so the friction becomes stronger. Read More
Is Sand and Abiotic Factor?
How do you get dry sand and water from wet sand?
We can take some wet sands then, smash the sand so that the water will come out. In that way, we can get both water and dry sand. Read More
If you have sand in your gerbils cage how long is it until you have to change it?
if it is wet take out the wet sand you can sift and reuse sand but 5 times max Read More
What will happen to friction if the road is wet?
Which has most friction - oil water or sand?
What surface has the least amount of friction?
The surfaces used as the measure of lowest friction are generally wet ice on wet ice. Some materials, such as superfluid Helium III have no measurable friction. Read More
Why is walking on wet ice difficult?
Because there is no friction on wet ice. Read More
Which force is weakened when the floor is wet?
How many tons does a cubic meter of wet sand weigh?
It will depend on (a) the bulk density of the dry sand and (b) the moisture content of the wet sand. Read More
What kind of sand is in the pacific ocean?
Does sand weigh more when it is wet or dry?
Sand, dirt, and other dry things weigh more if it is wet. Read More
Is the coefficient of dry friction greater than coefficient of wet friction?
When you walk across dry sand you sink when you walk across wet sand you do not sink why?
As the dry sand is loosely packed/coupled with each other thus the substancial force which are required to hold each granual is less as compared to the wet sand. when the sand is wet the forces of attraction increases as the each granual of the sand is easily coupled increasing the substancial force. thus a person can walk over wet sand rather than on a dry sand Read More
Does oil work better then water in reducing friction between two surfaces?
Yep- it a proven fact. Oil is used to reduce friction . Water is used to cool the heat of friction. To add to that oil acts as a lubricant reducing friction. Water actually increases friction because of its surface tension. Water is sticky, for example when you go to the beach that is why sand sticks to your feet only when they are wet, not when they are dry. Read More
If sand is rubbed together what is the source of the energy which heats the sand?
What is the density of wet sand?
That depends on the type and grade of the sand Read More
Is there dry sand beneath the wet sand at the bottom of the ocean?
When sand is mixed with water what mixture will be formed?
Is the Olympic hockey pitch supposed to be wet?
Yes, the water helps reduce friction on the surface which helps a dimpled hockey ball travel more smoothly along the ground and not bounce to create a danger to participants on the pitch. It also helps reduce friction burns and surface scrapes on skin when players fall. Sand Based and Sand Dressed pitches are never watered. Read More
What is the density of sand?
Density of sand can vary depending on the grain size and moisture content and how tightly it is compacted If you dont need very accurate densities the following should help Sand, wet 1922 Sand, wet, packed 2082 Sand, dry 1602 Sand, loose 1442 Sand, rammed 1682 Sand, water filled 1922 Sand with Gravel, dry 1650 Sand with Gravel, wet 2020 density of sand will vary depending upon the condition.that is for wet,dry,gravel.. Read More
Does sand conduct electricty?
Dry sand won't conduct electricity. Wet sand will. Read More
Why does sand on ice keep you from slipping?
because sand makes friction from the ice Read More
How many cubic yards of sand make 1 ton?
It depends. Is it: Sand, wet, packed Sand, dry Sand, loose Sand, rammed Sand, water filled Sand w/ Gravel, dry Sand w/ Gravel, wet Read More
What happens to sand when it gets wet?
When sand gets wet it becomes denser. It does not have a physical change other then becoming denser and heavier. Read More
Why it is dangerous to race on wet racing track?
because there is less friction on wet tracks. Read More
How do you use friction in a sentence?
I made friction by rubbing the sand paper against the cabinet. Read More
What is the weight of one cup of sand?
Wet sand would be heavier than dry sand. Read More
Does wet sand sink?
No, sand will be suspended in the water to form a solution. Read More
How can you not lessen friction?
Which has more friction sand or concrete?
Why sand and blood cells cannot be filtered?
it has much friction between the particles of sand and blood cells and blood cells are more concentrated than sand thats why sand and blood cells can not be filtrated. Sand consists of beeds so this beeds actually bring about this more friction. Read More
What friction is there when people slip on a clean wet floor?
This type of friction is called lubricated friction. Lubricated friction is a type of fluid friction where a fluid separates two solid surfaces. Read More
Which has less friction a dry road or wet road?
Can moon sand get wet?
What is an example of friction?
friction is what makes it hard to rub two pieces of sand paper together Read More
Weird fact about eels?
that eels can travl on wet grass and wet sand Read More
In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow.
The Darcy friction factor is also known as the Darcy–Weisbach friction factor, resistance coefficient or simply friction factor; by definition it is four times larger than the Fanning friction factor.[1]
- 2Flow regime
- 3Choosing a formula
- 4Approximations of the Colebrook equation
Notation[edit]
In this article, the following conventions and definitions are to be understood:
- The Reynolds number Re is taken to be Re = VD / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where
- ν is the kinematic viscosity μ / ρ, with μ the fluid's viscosity, and ρ the fluid's density.
- The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe (inside) diameter.
- f stands for the Darcy friction factor. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D.
- The log function is understood to be base-10 (as is customary in engineering fields): if x = log(y), then y = 10x.
- The ln function is understood to be base-e: if x = ln(y), then y = ex.
Flow regime[edit]
Which friction factor formula may be applicable depends upon the type of flow that exists:
- Laminar flow
- Transition between laminar and turbulent flow
- Fully turbulent flow in smooth conduits
- Fully turbulent flow in rough conduits
- Free surface flow.
Transition flow[edit]
Transition (neither fully laminar nor fully turbulent) flow occurs in the range of Reynolds numbers between 2300 and 4000. The value of the Darcy friction factor is subject to large uncertainties in this flow regime.
Turbulent flow in smooth conduits[edit]
The Blasius correlation is the simplest equation for computing the Darcy frictionfactor. Because the Blasius correlation has no term for pipe roughness, itis valid only to smooth pipes. However, the Blasius correlation is sometimesused in rough pipes because of its simplicity. The Blasius correlation is validup to the Reynolds number 100000.
Turbulent flow in rough conduits[edit]
The Darcy friction factor for fully turbulent flow (Reynolds number greater than 4000) in rough conduits can be modeled by the Colebrook–White equation.
Free surface flow[edit]
The last formula in the Colebrook equation section of this article is for free surface flow. The approximations elsewhere in this article are not applicable for this type of flow.
Choosing a formula[edit]
Before choosing a formula it is worth knowing that in the paper on the Moody chart, Moody stated the accuracy is about ±5% for smooth pipes and ±10% for rough pipes. If more than one formula is applicable in the flow regime under consideration, the choice of formula may be influenced by one or more of the following:
- Required accuracy
- Speed of computation required
- Available computational technology:
- calculator (minimize keystrokes)
- spreadsheet (single-cell formula)
- programming/scripting language (subroutine).
Colebrook–White equation[edit]
The phenomenological Colebrook–White equation (or Colebrook equation) expresses the Darcy friction factor f as a function of Reynolds number Re and pipe relative roughness ε / Dh, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.[2][3] The equation can be used to (iteratively) solve for the Darcy–Weisbach friction factor f.
For a conduit flowing completely full of fluid at Reynolds numbers greater than 4000, it is expressed as:
or
where:
- Hydraulic diameter, (m, ft) – For fluid-filled, circular conduits, = D = inside diameter
- Hydraulic radius, (m, ft) – For fluid-filled, circular conduits, = D/4 = (inside diameter)/4
![Factor Factor](/uploads/1/2/5/7/125729763/981096114.png)
Note: Some sources use a constant of 3.71 in the denominator for the roughness term in the first equation above.[4]
Solving[edit]
The Colebrook equation is usually solved numerically due to its implicit nature. Recently, the Lambert W function has been employed to obtain explicit reformulation of the Colebrook equation.[5][6][7]
or
will get:
then:
Expanded forms[edit]
Additional, mathematically equivalent forms of the Colebrook equation are:
- where:
- 1.7384... = 2 log (2 × 3.7) = 2 log (7.4)
- 18.574 = 2.51 × 3.7 × 2
- where:
and
- or
- where:
- 1.1364... = 1.7384... − 2 log (2) = 2 log (7.4) − 2 log (2) = 2 log (3.7)
- 9.287 = 18.574 / 2 = 2.51 × 3.7.
- where:
The additional equivalent forms above assume that the constants 3.7 and 2.51 in the formula at the top of this section are exact. The constants are probably values which were rounded by Colebrook during his curve fitting; but they are effectively treated as exact when comparing (to several decimal places) results from explicit formulae (such as those found elsewhere in this article) to the friction factor computed via Colebrook's implicit equation.
Equations similar to the additional forms above (with the constants rounded to fewer decimal places, or perhaps shifted slightly to minimize overall rounding errors) may be found in various references. It may be helpful to note that they are essentially the same equation.
Free surface flow[edit]
Another form of the Colebrook-White equation exists for free surfaces. Such a condition may exist in a pipe that is flowing partially full of fluid. For free surface flow:
The above equation is valid only for turbulent flow. Another approach for estimating f in free surface flows, which is valid under all the flow regimes (laminar, transition and turbulent) is the following[8]:
where a is:
and b is:
where Reh is Reynolds number where h is the characteristic hydraulic length (hydraulic radius for 1D flows or water depth for 2D flows) and Rh is the hydraulic radius (for 1D flows) or the water depth (for 2D flows). The Lambert W function can be calculated as follows:
Approximations of the Colebrook equation[edit]
Haaland equation[edit]
The Haaland equation was proposed in 1983 by Professor S.E. Haaland of the Norwegian Institute of Technology.[9] It is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation, but the discrepancy from experimental data is well within the accuracy of the data.
The Haaland equation[10] is expressed:
Swamee–Jain equation[edit]
The Swamee–Jain equation is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation.[11]
Serghides's solution[edit]
Serghides's solution is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation. It was derived using Steffensen's method.[12]
The solution involves calculating three intermediate values and then substituting those values into a final equation.
The equation was found to match the Colebrook–White equation within 0.0023% for a test set with a 70-point matrix consisting of ten relative roughness values (in the range 0.00004 to 0.05) by seven Reynolds numbers (2500 to 108).
Goudar–Sonnad equation[edit]
Goudar equation is the most accurate approximation to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation. Equation has the following form[13]
Brkić solution[edit]
Brkić shows one approximation of the Colebrook equation based on the Lambert W-function[14]
The equation was found to match the Colebrook–White equation within 3.15%.
Blasius correlations[edit]
Early approximations for smooth pipes[15] by Paul Richard Heinrich Blasius in terms of the Moody friction factor are given in one article of 1913:[16]
- .
Johann Nikuradse in 1932 proposed that this corresponds to a power law correlation for the fluid velocity profile.
Mishra and Gupta in 1979 proposed a correction for curved or helically coiled tubes, taking into account the equivalent curve radius, Rc:[17]
- ,
with,
where f is a function of:
- Pipe diameter, D (m, ft)
- Curve radius, R (m, ft)
- Helicoidal pitch, H (m, ft)
- Reynolds number, Re (dimensionless)
valid for:
- Retr < Re < 105
- 6.7 < 2Rc/D < 346.0
- 0 < H/D < 25.4
Table of Approximations[edit]
The following table lists historical approximations to the Colebrook–White relation[18] for pressure-driven flow. Churchill equation[19] (1977), Cheng (2008)[20] and Bellos et al. (2018)[21] equations return an approximately correct value for friction factor in the laminar flow region (Reynolds number < 2300). All of the others are for transitional and turbulent flow only.
Equation | Author | Year | Range | Ref |
---|---|---|---|---|
Moody | 1947 | |||
| Wood | 1966 | ||
Eck | 1973 | |||
Swamee and Jain | 1976 | |||
Churchill | 1973 | Not specified | ||
Jain | 1976 | |||
| Churchill | 1977 | ||
Chen | 1979 | |||
Round | 1980 | |||
Barr | 1981 | |||
| Zigrang and Sylvester | 1982 | ||
Haaland[10] | 1983 | |||
| Serghides | 1984 | ||
if then and if then | Tsal | 1989 | ||
Manadilli | 1997 | |||
Romeo, Royo, Monzon | 2002 | |||
| Goudar, Sonnad | 2006 | ||
| Vatankhah, Kouchakzadeh | 2008 | ||
| Buzzelli | 2008 | ||
where | Cheng | 2008 | all flow regimes | |
Avci, Kargoz | 2009 | |||
Evangelides, Papaevangelou, Tzimopoulos | 2010 | |||
Fang | 2011 | |||
, | Brkić | 2011 | ||
| S.Alashkar | 2012 | ||
where | Bellos, Nalbantis, Tsakiris | 2018 | all flow regimes |
References[edit]
- ^Manning, Francis S.; Thompson, Richard E. (1991). Oilfield Processing of Petroleum. Vol. 1: Natural Gas. PennWell Books. ISBN978-0-87814-343-6., 420 pages. See page 293.
- ^Colebrook, C. F.; White, C. M. (1937). 'Experiments with Fluid Friction in Roughened Pipes'. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 161 (906): 367–381. Bibcode:1937RSPSA.161..367C. doi:10.1098/rspa.1937.0150.
Often erroneously cited as the source of the Colebrook-White equation. This is partly because Colebrook (in a footnote in his 1939 paper) acknowledges his debt to White for suggesting the mathematical method by which the smooth and rough pipe correlations could be combined.
- ^Colebrook, C F (1939). 'TURBULENT FLOW IN PIPES, WITH PARTICULAR REFERENCE TO THE TRANSITION REGION BETWEEN THE SMOOTH AND ROUGH PIPE LAWS'. Journal of the Institution of Civil Engineers. 11 (4): 133–156. doi:10.1680/ijoti.1939.13150. ISSN0368-2455.
- ^VDI Gesellschaft (2010). VDI Heat Atlas. Springer. ISBN978-3-540-77876-9.
- ^More, A. A. (2006). 'Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes'. Chemical Engineering Science. 61 (16): 5515–5519. doi:10.1016/j.ces.2006.04.003.
- ^Brkić, D. (2012). 'Lambert W Function in Hydraulic Problems'(PDF). Mathematica Balkanica. 26 (3–4): 285–292.
- ^Keady, G. (1998). 'Colebrook-White Formula for Pipe Flows'. Journal of Hydraulic Engineering. 124 (1): 96–97. CiteSeerX10.1.1.1027.8918. doi:10.1061/(ASCE)0733-9429(1998)124:1(96).
- ^Bellos, Vasilis; Nalbantis, Ioannis; Tsakiris, George (December 2018). 'Friction Modeling of Flood Flow Simulations'. Journal of Hydraulic Engineering. 144 (12): 04018073. doi:10.1061/(asce)hy.1943-7900.0001540. ISSN0733-9429.
- ^Haaland, SE (1983). 'Simple and Explicit Formulas for the Friction Factor in Turbulent Flow'. Journal of Fluids Engineering. 105 (1): 89–90. doi:10.1115/1.3240948.
- ^ abMassey, Bernard Stanford (1989). Mechanics of fluids. Chapman & Hall. ISBN978-0-412-34280-6.
- ^Swamee, P.K.; Jain, A.K. (1976). 'Explicit equations for pipe-flow problems'. Journal of the Hydraulics Division. 102 (5): 657–664.
- ^T.K, Serghides (1984). 'Estimate friction factor accurately'. Chemical Engineering Journal. 91 (5): 63–64. ISSN0009-2460.
- ^Goudar, C. T; Sonnad, J. R. (2008). 'Comparison of the iterative approximations of the Colebrook-White equation: Here's a review of other formulas and a mathematically exact formulation that is valid over the entire range of Re values'. Hydrocarbon Processing. 87 (8).
- ^Brkić, Dejan (2011). 'An Explicit Approximation of Colebrook's equation for fluid flow friction factor'(PDF). Petroleum Science and Technology. 29 (15): 1596–1602. doi:10.1080/10916461003620453.
- ^Massey, B. S. (2006). Mechanics of Fluids (8th ed.). Chapter 7 eq 7.5: Taylor & Francis. p. 254. ISBN978-0-415-36205-4.
- ^Trinh, Khanh Tuoc (2010), On the Blasius correlation for friction factors, arXiv:1007.2466, Bibcode:2010arXiv1007.2466T
- ^Bejan, Adrian; Kraus, Allan D. (2003). Heat Transfer Handbook. John Wiley & Sons. ISBN978-0-471-39015-2.
- ^Beograd, Dejan Brkić (March 2012). 'Determining Friction Factors in Turbulent Pipe Flow'. Chemical Engineering: 34–39.(subscription required)
- ^Churchill, S.W. (November 7, 1977). 'Friction-factor equation spans all fluid-flow regimes'. Chemical Engineering: 91–92.
- ^Cheng, Nian-Sheng (September 2008). 'Formulas for Friction Factor in Transitional Regimes'. Journal of Hydraulic Engineering. 134 (9): 1357–1362. doi:10.1061/(asce)0733-9429(2008)134:9(1357). ISSN0733-9429.
- ^Bellos, Vasilis; Nalbantis, Ioannis; Tsakiris, George (December 2018). 'Friction Modeling of Flood Flow Simulations'. Journal of Hydraulic Engineering. 144 (12): 04018073. doi:10.1061/(asce)hy.1943-7900.0001540. ISSN0733-9429.
Further reading[edit]
- Moody, L.F. (1944). 'Friction Factors for Pipe Flow'. Transactions of the ASME. 66 (8): 671–684.
- Brkić, Dejan (2011). 'Review of explicit approximations to the Colebrook relation for flow friction'(PDF). Journal of Petroleum Science and Engineering. 77 (1): 34–48. doi:10.1016/j.petrol.2011.02.006.
- Brkić, Dejan (2011). 'W solutions of the CW equation for flow friction'. Applied Mathematics Letters. 24 (8): 1379–1383. doi:10.1016/j.aml.2011.03.014.
- Brkić, Dejan; Ćojbašić, Žarko (2017). 'Evolutionary Optimization of Colebrook's Turbulent Flow Friction Approximations'. Fluids. 2 (2): 15. doi:10.3390/fluids2020015. ISSN2311-5521.
External links[edit]
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