1 Abstract Major and Minor Losses Caitlyn Collazo, Team 2 (1:00 pm) A Technovate fluid circuit system was used to determine the pressure drop across a pipe section and across an orifice. These pressure drops provide a way to find the friction factor acting on the pipe and the velocity of a flow. The friction factor is responsible for major losses in a piping system. The theoretical friction factor is slightly larger when compared to the experimental friction factor. The larger the pipe diameter the lower the velocity, and the smaller the pipe diameter the larger the velocity. The larger pipe diameter had a larger percent error when comparing the friction factors, at an average of 30 percent. While the smaller pipe diameter had a smaller percent error when comparing the friction factors, an average of 12 percent. On the other hand, a Edibon Energy Losses Module was used to determine the pressure drop in different fittings. The experimental and theoretical loss coefficients, K varied, with a 99 percent error to a 1 percent error. This shows that some fittings had larger losses than others. Introduction Friction head loss in piping systems is a huge part of irrigation design. The friction factors change based on the Reynolds number, or the type of flow such as laminar or transitional regimes, and the flow velocity (Allen 1973). Friction is directly related to pressure drop and head loss during flow. A pressure drop is due to viscous effects and represents an irreversible pressure loss in a system, and it is proportional to the viscosity, μ, of a fluid. If there was no friction, then the pressure drop would be zero. The head loss represents the additional height that the fluid needs to be raised by a pump to overcome all the frictional losses in the system. There are minor head losses and major head losses. The head loss is also related to viscosity, but also to the shear stress acting on the wall of the pipe (Cengel and Cimbala 2014). Orifices are accurate flow measurement devices, however the flow measurement accuracy decreases with head loss (Trout 1986). An orifice is used to determine the flow rate, to determine the volumetric flow rate and the velocity of a flow. An orifice meter is a type of flowmeter causing significant head loss, and permanent pressure loss, which is based on the principle of obstruction flowmeters (Cengel and Cimbala 2014). A typical piping system includes pipes of all sorts of diameters connected by all sorts of fittings and elbows. These are mainly used to control the flow rate of the system. Major losses are typically head losses in straight pipe sections, while minor losses are head losses within long pipes. In some cases, minor losses may be greater than major losses (Cengel and Cimbala 2014). Major head losses are dependent on the friction factor, and the friction factor is dependent on the Reynolds number (Allen 1973). The minor losses are expressed in terms of the loss coefficient, K, also called the resistance coefficient. The loss coefficient depends on the geometry of the component as well as, the Reynolds number, just like the friction factor (Cengel and Cimbala 2014). 1
2 2 Objective The objective of this lab is to (1) measure the effect that the pipe diameter has on the friction factor, or major loss, and (2) the effect that the fitting type has on minor losses due in pipes. Methods and Materials Major Losses A Technovate fluid circuit system was used to obtain the pressure drop across a pipe section and the pressure drop across the orifice. Valve 52 was used to control the flow rate through the system. Six readings for each of the pipe sections were recorded, and this was repeated for another pipe with a different diameter. A pipe diameter of m and m was used in order to find the pressure drop across both the pipe section and orifice. However, the pressure drop (Eqn. 1) across the orifice is used to calculate the volumetric flow rate (Q) through a pipe given by (Eqn. 2). P orifice = ρg(h 2 h 1 ) (Pa) (1) Where, ρ = 1000 kg/m 3, the density of water g = 9.81 m/s 2, gravity h2 h1, is the absolute value in the change of height across the orifice (m) Q = A o C d 2 P orifice ρ(1 β 4 ) ( m3 s ) (2) Where, A0 is the orifice area of the pipe given by πd orifice 2 (m 2 ), 4 Cd = 0.656, the drag coefficient Porifice is the calculated orifice pressure drop (Pa) ρ = 1000 kg/m 3, the density of water β = d/d (unitless), the ratio of throat diameter to pipe diameter dorifice = 0.625, and Dleading to orifice = The pressure drop across a pipe section or the difference in height was used to calculate the head loss (hl), given by the (Eqn. 3) h L = P (m) ρg Where P, is the pressure drop across the pipe section, ρgh ρ = 1000 kg/m 3, the density of water, and g = 9.81 m/s 2, gravity Once the volumetric flow rate (Q) was obtained, the velocity of the flow is the volumetric flow rate divided by the area of the pipe. The velocity of the flow is used to determine the experimental friction factor. The experimental friction factor was obtained by using (Eqn. 4) and solving for f after having found the head loss across the pipe and velocity of the flow. (3)
3 3 V 2 h L = f L D 2g Where, hl is the calculated head loss (m) L = m, the length for the pipe D is the diameter for the specific pipe (m) V 2 is the velocity squared (m/s) g = 9.81 m/s 2, gravity (4) The flow through the pipes with different diameters were determined by calculating the Reynolds number (Eqn. 5). If the flow is turbulent, which has a Reynolds number greater than 4000, then the Colebrook Equation (Eqn.6) was used to determine the theoretical friction factor. Re = ρvd μ Where ρ = kg/m 3, density at 20ºC V, the velocity of the flow D, the diameter of the pipe μ = kg/m 3, dynamic viscosity at 20ºC (5) ε 1 f = 2.0log ( D Re f ) (6) Where, ε = m, the roughness for a copper pipe D, the diameter of the pipe The calculated experimental and theoretical friction factors were then plotted versus the velocity squared. Minor Losses The Edibon Energy Losses in Bends Module was used to calculate the minor losses. The module contained the following fittings: long elbow (1&2), sudden enlargement from 0.02m to 0.04m (3&4), sudden contraction from 0.04m to 0.02m (5&6), medium elbow (7&8), short elbow (8&9) and right-angle fittings (11&12). The control valve was used to measure the flow rate. Six readings for the flow rate were obtained corresponding with pressure readings until the tap 12 pressure drop is about 0 inches of water, and the manometer reading difference between taps 11 and 12 that vary from 5 mm to 60 mm. The head loss was calculated by taking the difference at each of the fittings. The velocity was calculated by using the volumetric flow rate divided by area. The experimental K value is determined by (Eqn. 7).
4 Friction Factor, f 4 h L = K V2 2g Where, hl is the calculated head loss V 2 is the velocity g = 9.81 m/s 2, gravity (7) The head loss for each fitting is compared to the velocity squared value in a plot, and the slope of the lines are determined to be the experimental K values multiplied by 2g. The theoretical K values are determined by using Table 8-4 (Cengel and Cimbala 2014). Results and Discussion Major Losses The theoretical friction factor has a higher value compared to the experimental friction factor for both pipes with diameters m and m, shown by Figures 1 and 2. The friction factor decreases as the velocity for the flow increases. For the larger pipe, the percent error was much larger, when compared to the smaller pipe. The percent error ranged from 22 percent to 65 percent for a diameter of m, while the percent error for the smaller pipe ranged from 10 percent to 12 percent. Experimental Friction Factor Theoretical Friction Factor Velocity, V 2 ((m s -1 ) 2 ) Figure 1: The Experimental and Theoretical Friction Factors versus the Velocity squared value for a pipe with a diameter of m. The experimental and theoretical friction factors closely relate for the smaller pipe diameter, shown by Figure 2. The m diameter pipe had an average of 12 percent error. The smaller pipe also has a much higher velocity flowing through.
5 Friction Factor, f 5 For both pipe diameters, the theoretical friction factor is larger. This could indicate that the Technovate fluid circuit system needs to be calibrated in order to obtain better readings to cut down on the percent error. Experimental Friction Factor Theoretical Friction Factor Velocity, V 2 ((m s -1 ) 2 ) Figure 2: The Experimental and Theoretical Friction Factors versus the Velocity squared value for a pipe with a diameter of m. Minor Losses The head loss at each fitting versus the velocity squared values provides a set of data points, where a trendline with an intercept of zero is shown. This trendline reveals a slope, which is the K value divided by 2 times gravity. The slopes shown in Figure 3 are the experimental K values, which the minor losses depend upon.
6 Head Loss, H L (m) 6 Long Bend (m) Wide (m) Narrow (m) Elbow (m) Short Bend (m) Mitre (m) Linear (Long Bend (m) ) Linear (Wide (m)) Linear (Narrow (m) ) Linear (Elbow (m)) Linear (Short Bend (m) ) Linear (Mitre (m) ) y = 0.055x y = x y = x y = x y = x y = 0.011x Velocity, V 2 ((m s -1 ) 2 ) Figure 3: The Head Loss, hl, at each fitting versus the Velocity Squared, V 2. The experimental K values are compared to the theoretical K values in Table 1. The fittings with a sudden enlargement or contraction have much larger percent errors compared to the elbows with lower percent errors. The large percent error could be caused by calculation error when dealing with the area while enlargement or contraction occurs. Table 1: Comparing the Experimental K Values and the Theoretical K Values, while showing their percent error. Fittings Experimental K Values Theoretical K Values Percent Error % Long Bend Widening Narrowing Elbow Short Bend Mitre Conclusions Pipe diameter does influence friction factors, or major losses, and has an effect of fitting type on minor losses due to the loss coefficient, K. The experimental and theoretical friction factors for a small pipe diameter, in this instance m, and a great velocity had a lower percent error, an average of 12 percent. The larger pipe diameter, m, and a lower velocity had a larger
7 percent error with an average of 30 percent. The friction factors result in a major loss for the piping system. The loss coefficient, K, had an impact with minor losses in a piping system. The experimental and theoretical loss coefficients varied for the fitting, resulting in high percent errors, percent, and low percent error, 1.91 percent. This shows that some fittings have greater losses than others. 7
8 8 References Cengel, Y., and J. Cimbala. Fluid Mechanics: Fundamentals and Applications. 3 rd ed., McGraw Hill, Allen, R. G Relating The Hazen Williams and Darcy Weisbach Friction Loss Equations for Pressurized Irrigation. ASAE Vol 12. Trout, J Orifice Plates for Furroe Flow Measurment Part II Design and Field Use. ASAE. Vol. 29