Dear Roland,

What you wrote is incorrect. This is not the right relationship for pressure drop.

Considering the Darcy-Weisbach formula, we can write that the head loss is :

dh= (fL/D)x(V^2)/2g

The pressure drop is then : dp = rhoxgxdh

That is : dp = rhoxfx L x('V^2)/(2D)

You can see that the constant g is simplified and does not intervene in the pressure drop according to the Darcy-Weisbach relation.

Regards

For the Hagen-Poiseuille formula, The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation.

The Hazen-Williams formula should be strongly discouraged. It was demonstrated the inaccuracies of the Hazen-Williams equation. Not only inaccurate, but the Hazen-Williams equation is also conceptually incorrect.

The Darcy-Weisbach relation, based on the coefficient of friction in the sense of Colebrook-White, is the most valid. The only disadvantage is that the Colebrook-White relationship is implicit. But, at present, there are extremely reliable approximate relationships.

Regards

The Darcy-Weisbach equation with the Moody diagram is considered to be the most accurate model for estimating frictional head loss for a steady pipe flow The Hazen-Williams formula is empirical and lacks a theoretical basis. The Hazen-Williams method is only valid for water flow - the Darcy Weisbach method should be used for other liquids or gases.

I think Hazen–Williams

Darcy-Weisbach

Why the Hazen-Williams Equation is conceptually incorrect :

According to the Hazen-Williams Equation, the pressure drop dp can be written as dp = 6.824xrhoxgxLx(V^1.85)/[(C^1.85)x(D^1.167)]

Where : rho is the fluid mass density and g is the gravitational acceleration.

The above equation leads to the illogical inference that in pipe flow the pressure drop depends on the gravitational acceleration.

After that, some people still advise us to use the Hazen-Williams equation !!

Regards

Why the Hazen-Williams Equation is conceptually incorrect :

According to the Hazen-Williams Equation, the pressure drop dp can be written as dp = 6.824xrhoxgxLx(V^1.85)/[(C^1.85)x(D^1.167)]

Where : rho is the fluid mass density and g is the gravitational acceleration.

The above equation leads to the illogical inference that in pipe flow the pressure drop depends on the gravitational acceleration.

After that, some people still advise us to use the Hazen-Williams equation !!

Regards

Dear Prof. Bachir Achour ,

Although I wholeheartedly agree with your first comment (advocating the use of Darcy-Weisbach equation), I would like to point out a minor flaw (in my humble opinion) regarding your last comment. It sounds technically incorrect to mention the acceleration constant 'g' here as a problem, since, even when one uses Darcy-Weisbach equation, the head loss (or pressure drop) will still be calculated using the same constant, that is: dP = (f/D)*(V^2/2g), where f would be the friction factor.

However, I believe Veli Süme missed the point. Actually, it is pretty straight to see from the literature that most head loss formulas were derived from empirical considerations. As such, they 'lack' somehow some physical basis in their theoretical development, and they obviously carry some assumptions that might not be true in specific cases. This is pretty much unsurprising since those who developed these equations were mostly interested in their practical use, for which these formulas provide fast and quite accurate approximations.

The Darcy-Weisbach formulation is the one which is the most sound, theoretically, and moreover, has a physical basis. It accounts for the flow regime (laminar, turbulent), and also both the internal fluid shear stress and the pipe wall roughness in evaluating the fluid friction factor. This is definitely the reason for what it is regarded as the most accurate.

Best,

Roland.

Dear Roland,

What you wrote is incorrect. This is not the right relationship for pressure drop.

Considering the Darcy-Weisbach formula, we can write that the head loss is :

dh= (fL/D)x(V^2)/2g

The pressure drop is then : dp = rhoxgxdh

That is : dp = rhoxfx L x('V^2)/(2D)

You can see that the constant g is simplified and does not intervene in the pressure drop according to the Darcy-Weisbach relation.

Regards

Dear Prof Bachir Achour , Perfect! And, my bad.

The Darcy-Weisbach formula gives the best results for calculating pressure drops.The Darcy-Weisbach formula gives the best results for calculating pressure drops. However, it is a little more difficult to apply with simple calculators.

The Darcy-Weisbach formula gives the best results for calculating pressure drops. However, it is a little more difficult to apply with simple calculators.

Hi all

The proporcionality between head loss and pressure drop considered by Bachir, hold for a horizontal pipe with constant diameter. If the pipe (assumed with constant diameter) is vertical or even inclined relative to the horizontal, the head loss for up flow and down flow will be the same (for the same flow rate, pipe, fluid and temperature) as that of the horizontal setup. However the pressure drop will be greater for up flow and lower for down flow. This follows from the Mechanical Energy Equation often referred to as Extended Bernoulli Equation.

Dear Peçanha,

Nothing indicates in my writings that it is exclusively about horizontal pipe. to convert the head loss into pressure loss, the head loss should be multiplied with the density of the fluid and the acceleration due to gravity. For incompressible fluids, we then use the extended Bernoulli theorem, which is written:

V1^2/(2g) +z1+P1/(rhoxg)=v2^2/(2g)+z2+P2/(rhoxg)+dh

In the case of an incompressible fluid, if the section of the pipe is constant, then the velocity is also constant. The altitude z being imposed by the installation of the pipe, it can be seen that the pressure drop results in a reduction in pressure.

A more general relationship will be written as:

V1^2/(2g) +z1++P1/(rhoxg)=v2^2/(2g)+z2+P2/(rhoxg)+dP/(rhoxg)

Where dP=rhoxgxdh

Regards

Dear Bachir

Of course you can express flow head loss in pressure units. However, this doesn’t transform the head loss into the associated pressure drop existing in the pipeline. In most real cases, the pipeline is a complex tridimensional assembly of pipes and fittings, frequently with pipes of various diameters. So, to avoid confusion by students, if you express flow head loss in pressure units you should call it friction pressure drop or viscous pressure drop, since it is determined by the fluid viscosity. In my experience is a commom (and wrong) saying by beginning students: “the only difference between head loss and pressure drop are the units”. Colloquially one can say that the pressure drop in such complex pipelines includes the head loss.

Regards.

Dear Rehan as far as I know The Darcy-Weisbach equation is more reliable. It can be used to calculate the major pressure or head loss due to friction in ducts, pipes or tubes

The Darcy-Weisbach equation with the Moody diagram is considered to be the most accurate model for estimating frictional head loss for a steady pipe flow. Since the Darcy-Weisbach equation requires iterative calculation an alternative empirical head loss calculation like the Hazen-Williams equation may be preferred:

h100ft = 0.2083 (100 / c)1.852 q1.852 / dh4.8655                          where h100ft = friction head loss in feet of water per 100 feet of pipe (fth20/100 ft pipe) c = Hazen-Williams roughness constant q = volume flow (gal/min) dh = inside hydraulic diameter (inches)

Note that the Hazen-Williams formula is empirical and lacks a theoretical basis. Be aware that the roughness constants are based on "normal" conditions with approximately 1 m/s (3 ft/sec).

Dear Rehan,

It cannot be differentiated which equation one is better among them.

The Darcy Weisbach formula takes into account the internal roughness (f), velocity (V) and hydraulic slope (L) in computing the headloss for a pipe. Whereas, Hazen-Williams formula uses only the dimensionless "C" factor for computing headloss. Poiseuille's law applies to laminar flow of an incompressible fluid of viscosity through a tube of length and radius.

The Hazen–Williams equation is an empirical relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe systems such as fire sprinkler systems, water supply networks, and irrigation systems. The Hazen–Williams equation has the advantage that the coefficient C is not a function of the Reynolds number, but it has the disadvantage that it is only valid for water. Also, it does not account for the temperature or viscosity of the water.

In fluid dynamics, the Darcy–Weisbach equation is an empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy–Weisbach friction factor, friction factor, resistance coefficient, or flow coefficient.

In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. Poiseuille's law applies to laminar flow of an incompressible fluid of viscosity through a tube of length and radius . The direction of flow is from greater to lower pressure. Flow rate is directly proportional to the pressure difference , and inversely proportional to the length of the tube and viscosity of the fluid.

If I see from literature,

Darcy-Weisbach and Hazen-Williams equations, for cold and hot water flows through plastic pipes. Corresponding to water temperatures ranging from 20ºC to 60ºC, hydraulic models developed to estimate the head loss in the pipes for various pipe diameters (15 mm to 50 mm) and volume flowrates (0.25 lps to 2 lps). The head loss values obtained by the Darcy-Weisbach and Hazen-Williams equations were used to establish the correlation between them. The correlation coefficient between both equations was found to be 0.999, while the R 2 value for the trend-line of head loss values obtained by these equations was 0.9993. This relationship would be very useful for the manufacturers and designers for the mutual conversion of head loss values obtained by these equations.

The relation is valid for hot and cold water plastic pipes within the diameter range 15 mm - 50 mm and water temperature 20º C - 60º C. Steel pipes in general have a very high rate of thermal conductivity, and according to a few studies, the temperature of the external surface of a metallic pipe is the same as that of the water flowing inside it. But on the other hand, the thermal conductivity of plastic pipes considered for this research is almost 50-60% less than that of steel pipes. For instance, Galvanized Iron (GI) pipe was considered for comparison having a Hazen-William Constant of 120. The developed relation is only valid for plastic pipes which are more commonly used and have a lot of benefits over other pipe materials.

It is better to have a good question where these equations could be used?

Hope it is helpful for you.

Ashish

I believe there is no longer any hesitation. Darcy-Weisbach's relationship has proven itself in all the hydraulic laboratories of the world. Not only it applies to pipes-flow but it is also extensible to free surface flow, uniform and non-uniform flow. Hundreds of scientific articles dealing with its history and its capacities to deal effectively with hydraulic problems have been devoted to this relationship. The Darcy-Weisbach equation has a long history of development, which started in the 18th century and continues to this day. While it is named after two great engineers of the 19th century, many others have also aided in the effort.

In a word, it is an indispensable formula if we wish to engineer systems that move liquids or gasses from one point to another. Thus, because of its general accuracy and complete range of application, the Darcy-Weisbach equation should be considered the standard and the others should be left for the historians. Liou (1998) presented an interesting discussion on the topic. It is unfortunate that we continue to use less precise and conceptually incorrect empirical formulas such as the Hazen-Williams formula. We have demonstrated this in a previous comment.

Regards

Darcy-Weisbach. Hagen–Poiseuille is used for calculation of laminar flow friction facor in the Darcy-Weisbach equation (for turbulent flow friction, empirical Colebrook formula can be used). Hazen-Williams equation should be avoided.

Hello Mr Rehan

I wanted to answer to your question, but when I found Mr. Bachir Achour answers, I stopped because I agreed on everything he said

Best regard

Dear sir,

Theoretically we can use all the above equations provided suffient data is available. In my opinion, it is difficult to predict the exact head loss from any of the above equations, unless we measure practically. In my experience, pipe internal surface textures are quite different from what we are assuming. It depends on flowing fluid nature, dissolved gases, water chemistry, suspended particles, velocity, temperature, size of pipe, orientation, etc.

Dear Nelaturi,

Can you please clarify your idea better?

"In my experience, pipe internal surface textures are quite different from what we are assuming. It depends on flowing fluid nature, dissolved gases, water chemistry, suspended particles, velocity, temperature, size of the pipe, orientation, etc."

Are you talking about the calculation of the pressure drop or head loss that is the subject of the question, or about the texture of the internal surface of the pipe?

Regards

I am a mechanical maintenance engineer and also NDT inspector from large scale industry. Last 20 years I came across various piping and equipment for the services of raw water. Filter water, process water, boiler feed, condensate, acidic and alkali fluids, M-class fliuds, effluents, etc.During inspection of piping, it is observed that internal surface textures, roughnrss and profiles are different for different conditions, which are causing head loss during pipe flow conditions.

Dear Nelaturi,

We are not talking about the same thing here. These are pipes supplying a drinking water network. Where drinking water comes from: springs; groundwater; surface water. This water needs to be treated to become potable and be distributed by the network. The water undergoes many paths and treatments to be routed, via the distribution network, to our tap. There is no sediment, as these are removed during processing. The pipes scale up over time. we can know the height of the roughness as a function of time. These roughness are taken into account in the calculation of the head loss and this calculation is very well done with the Darcy-Weisbach relation. In this relation, the coefficient of friction of Colebrook-White is governed by a relation drawn from the experiment. The temperature of the water is taken into account because it conditions the value of the viscosity which can be easily calculated. Viscosity is an important parameter of the Colebrook-White relationship through the Reynolds number.

Finally, the flow of water in the distribution pipes is monophasic.

Regards

I think the Darcy-Weisbach equation is more reliable or may be its more workable in the field.

I think its depending on the type of fluid