Major and Minor Losses in pipes
Roll No. : 110517 Section : M6
Head Losses Major Losses Minor Losses Example Problem Total Head Loss Friction Loss Extended Bernoulli’s equation
In the analysis of piping systems, pressure losses are commonly expressed in terms of the equivalent fluid column height called Head Losses (hL). It also represents the additional height that the fluid needs to be raised by a pump inorder to overcome the frictional losses in the pipe
PL hL g 2gd
2 fLVavg
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Differential Pressure Gaugemeasure ΔP
L
ρ
V
ε Pipe
D
μ
Physical problem is to relate pressure drop to fluid parameters and pipe geometry
P( ,V , L, , D, )
Using dimensional analysis we can show that
VD L , , 1 2 D D V 2 P
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Apart from major loss due to friction, there are also other forms of losses which are caused by changes in internal pipe geometries and by fitted components. These types of losses are referred to as minor losses. There are four types of minor losses:
Sudden or gradual flow expansion and flow contraction, Entrance and exit flows to and from reservoirs or tanks, Bends, elbows, junctions and other fittings, Valves, including those completely opened or partially closed.
Piping systems include fittings, valves, bends, elbows, tees, inlets, exits, enlargements, and contractions. These components interrupt the smooth flow of fluid and cause additional losses because of flow separation and mixing. The minor losses associated with these components:
KL is the loss coefficient. — Is different for different components. — Typically provided by manufacturers.
V2 hm K 2g 7
Minor losses are usually expressed in terms of the loss coefficient K L
The loss coefficient of a component (such as the gate valve shown) is determined by measuring the pressure loss it causes and dividing it by the dynamic pressure in the pipe.
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Ans: 169 kPa
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Total head loss in a system is comprised of major losses (in the pipe sections) and the minor losses (in the components)
i pipe sections
j components
If the entire piping system has a constant diameter, then
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For laminar flow in rough pipes, the friction factor f is dominantly caused by viscous friction due to molecular interaction. Hence, we can use Eq. (8.12) for all occasions involving laminar flow. However, for turbulent flow, the profile at the core of the pipe is close to inviscid profile and the friction factor f is much due to the existence of viscous sublayer near the wall. Thus, if the wall surface is rougher, the resulting viscous sublayer is thicker. The roughness of a pipe is measured in length which is defined as equivalent roughness . The values of for typical pipes are listed in Table 8.1.
Table 8.1 Equivalent Roughness for Typical New Pipes 11
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For turbulent flow, the friction factor f can be obtained by using the graphical representation of the Colebrook formula which is the Moody chart as shown in Figure 8.11
Table 8.11: The moody chart 12
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In some texts, the same experimental data are refitted to a simpler form of correlation which can be solved directly with 2% error. This correlation is known as the Haaland formula which takes the following form: / D 1.11 6.9 1 1.8 log 3 . 7 Re f
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After knowing the friction factor f for the pipe, we can calculate the major head loss due to friction for a fluid flowing in the pipe. If fluid properties, and , pipe length and relative roughness of the pipe wall are all known, provided that other variables are also known, the problem can be one of the following types:
1.
Determine pressure loss p or friction head loss hf,
2.
Determine volumetric flow-rate Q or average velocity V,
3.
Determine pipe diameter D.
After knowing f, then hf can be calculated via Eq. (8.11), V2 hf f D 2g 13
Based on the previous discussion, the pressure distribution along a pipe system can be characterized by using the extended Bernoulli's equation: 2
V1 P2 V22 gz1 ghA ghE ghL gz2 2 2 For a horizontal(z1 =z 2 ), fully-developed(V1 =V2 ), straight pipe system with no external power P1
(h A =h E =0), the pressure drop is related to the losses alone, that is, P1 P2 P ghL frictional losses + minor losses =f
L 1 ( V 2 ) K L ( 1 V 2 ) 2 D 2
Both the loss coefficient and the frictional factor can be determined using the empirical values available in standardized tables or charts in chapter 8. Special note: due to the non-uniformity of the velocity profiles inside a pipe, the kinetic energy terms in the extended Bernoulli's equation should be modified to include this effect. The kinetic energy coefficient, , is so defined in chapter 8.6.1. See equations 8.28 and 8.29 to get more information. 14
Courtesy: NIT Kurukshetra
