# FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4)

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1 FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) 1

2 1.0 Objectives The objective of this experiment is to calculate loss coefficient (K value) and head loss (h L ) in pipes for different water flow rates, pipe diameters and pipe bends..0 Introduction As an incompressible fluid flows through a pipe, a friction force along the pipe wall is created against the fluid. The frictional resistance generates a continuous loss of energy or total head in the fluid and hence decreases the pressure of the fluid as it moves through the pipe. There are four factors that determine friction losses in pipe: i. The velocity of the fluid. ii. The size (inside diameter) of the pipe iii. The direction of flow in the pipe iv. The length of the pipe In addition to energy or head loss due to friction, there are always head losses in pipes due to an enlargement or contraction of the flow section, bends, junctions, and valves etc., which are commonly known as minor or small losses. When the direction of flow is altered or distorted, energy losses occur which are not recovered are dissipated in eddies and additional turbulence and finally lost in the form of heat. However, this energy must be supplied if the fluid is to be maintained in motion, in the same way, as energy must be provided to overcome friction. In practice, in long pipe lines of several kilometres the effect of minor losses may be negligible. For short pipeline the losses may be greater than those for friction. 3.0 Theory In Bernoulli's equation as shown below, h f represents the head loss due to friction between the fluid and the internal surface of the constant diameter pipe as well as the friction between the adjacent fluid layers p 1 /g + V 1 /g + Z1 = p / g + V /g + Z + h f (Eq. 1) This will result in a continuous change of energy from a valuable mechanical form (such as kinetic or potential energies) to a less valuable thermal form that is heat. This change of

3 energy is usually referred to as friction head loss, which represents the amount of energy converted into heat per unit weight of fluid. The head losses (h f ) in pipe due to friction can be determined using Darcy-Weisback equation; Turbulent flow h f = 4 flv (Eq. ) gd Laminar flow h f = 3 flq (Eq. 3) gd 5 Where: f = Friction factor L = Length V = Mean velocity (Q/A) g = Gravity D = Constant diameter The friction head loss for both laminar and turbulent flows can be expressed by similar formulas although the original derivation of each one is different: L V h f f (Eq. 4) D g In laminar flow, the friction factor is only a function of Reynolds number while for turbulent flow it is a function of Reynolds (R e ) number and the relative roughness of the pipe. VD Re (Eq. 5) where : density, V: average velocity, D: pipe inside diameter, : viscosity. Based on the nature of the flow, friction factor (f ) can be estimated using the following correlations Laminar flow f = 64 (Eq. 6) R e Turbulent Flow f = x R e -0.5 (Eq. 7) 3

4 Equation (7) is Blausius Equation and only valid for smooth pipe and 3000 < Re< The value of f for turbulent flow can be obtained experimentally from the Moody Chart. Moreover, for turbulent flow, the relationship between h f and V takes the form h f = K. V n (Eq. 8) where K is a loss coefficient and n ranges from 1.7 to.0 (depending on the value of Re and k s /D). This equation can be written as Log h f = Log K + n Log V (Eq. 9) in order to find K and n experimentally, using graph Experimentally, one can obtain the head loss by applying energy equation between any two points along a constant diameter pipe. This is done in Eq. 1 and by noticing that the pipe is horizontal and the diameter is constant. The pressure heads of a fluid between points, h 1 and h, are measured by using Piezometer tubes. The total head loss can be determined experimentally by applying the Bernoulli s equation as follows: h f = (P 1 - P ) /g = h 1 - h (Eq. 10) Energy losses are proportional to the velocity head of the fluid as it flows around an elbow, through an enlargement or contraction of the flow section, or through a valve. Experimental values for energy losses are usually reported in terms of a resistance or loss coefficient K as follows: h L = KV g (Eq. 11) where h L is the minor loss, K is the resistance or loss coefficient, and V is the average velocity of flow in the pipe in the vicinity where the minor loss occurs. The resistance or loss coefficient is dimensionless because it represents a constant of proportionality between the energy loss and the velocity head. The magnitude of the resistance coefficient depends on the geometry of the device that causes the loss and sometimes on the velocity of flow. Minor losses at sudden enlargement When a fluid flows from a smaller pipe into a larger pipe through a sudden enlargement, its velocity abruptly decreases, causing turbulence, which generates an energy loss. 4

5 where, V 1 = velocity at small cross-section (upstream) V = velocity at large cross-section (downstream) The minor loss (h L ) due to sudden enlargement of the pipe can be estimated by integrating the momentum, continuity and Bernoulli equations between positions 1 and to give V1 V h L (Eq. 1) g Substituting again for the continuity equation to get an expression involving the two areas, (i.e. V=V1(A1/A) gives KV1 h L (Eq. 13) g Where, K 1 A A 1 D 1 D 1 Minor losses at sudden contraction When a fluid flows from a larger pipe into a smaller pipe through a sudden contraction, the fluid streamlines will converge just downstream of the smaller pipe, known as vena contraction phenomena, creating a turbulence region from the sharp corner of the smaller pipe and extends past the vena contracta, which subsequently generates an energy loss. 5

6 In a sudden contraction, flow contracts from point 1 to point 1', forming a vena contraction. It is possible to assume that energy losses from 1 to 1' are negligible (no separation occurs in contracting flow) but that major losses occur between 1' and as the flow expands again If the vena contract area is A 1 =A c, then the minor loss (h L ) can be estimated by integrating the momentum, continuity and Bernoulli equations between positions 1 and to give h L 1 A A C V g (Eq. 14) The above equation is commonly expressed as a function of loss coefficient (K) and the average velocity (V ) in the smaller pipe downstream from the contraction as follows; Where KV h L (Eq. 15) g A K C 1 A As the difference in pipe diameters gets large (A1/A 0) then this value of K will tend towards 0.5 which is equal to the value for entry loss from a reservoir into a pipe. The value of K depends upon the ratio of the pipe diameters (D /D 1 ) as given below; D /D K

7 Minor Losses at elbow or bend pipe Losses in fittings such as elbow, valves etc have been found to be proportional to the velocity head of the fluid flowing. The energy loss is expressed in the general form, where, h L = KV g (Eq. 16) K = loss coefficient (dependent on the ratio of total angle of bending to radius of bending (R/d) of the curves as the bending occurs) Experimental determination of total head loss In the experiment the pressure heads before and after a fluid undergoing sudden change in pipe diameter or flow direction, h 1 and h, are measured by using Piezometer tubes. The total head loss (major and minor losses) can be determined experimentally by applying the Bernoulli s equation as follows: P 1 /g + V l / g + Z1 = P /g + V / g + Z + h L (Eq. 17) 7

8 h l + V l / g + Z1 = h + V / g + Z + h L (Eq. 18) and since Z 1 = Z, then V1 V h L h1 h (Eq. 19) g 4.0 Apparatus 8

9 9

10 10

11 Table of Water Dynamic Viscosity and Density at Different Temperatures Temperature ( o C) (kg/m 3 ) (x 10-3 N.s/m 3 )

12 5.0 Experimental Procedure 1) Open all outlet valves of pipes I, II, III, IV and V (valves are in parallel with the pipes). Make certain that the flow control valve in the base module is in closed position (turn clockwise). ) Switch on the pump and slowly open the control valve (turn counter-clockwise) until maximum, and wait for a while in order to remove any air bubble in the flowing pipe. 3) Identify which inlet flowing pressure (H 1 ) and outlet flowing pressure (H ) during installation of water manometer rubber tube 4) Determine the direction of water inflow and outflow through the pipe. 5) Perform measurement Adjust desired flow by way of inflow valve. Read off differential pressure as difference in height between the two water columns. Estimate mean value if reading fluctuates. When taking differentialpressure measurements, it is more important to achieve reproducible readings than absolute accuracy. During the process, if air bubbles present in the flowing pipe, the air will move through the water manometer rubber tube. Air bubbles will move to the peak of the higher tube. Remove the air bubbles up to the manometer glass tube. 6) Determine 5 (five) suitable flow rates Q (let the increment as large as possible). Record the values of H1 and H in millimeter (mm) of the inlet and the outlet of water manometer flowing pressures as Q is changed. 7) Operate on all the following types of flow. A) Experiment with Pipe I Friction losses at sudden enlargement and sudden contraction. B) Experiment with Pipe III and IV Friction losses in pipe branches (two types) C) Experiment with Pipe V Friction losses at pipe elbows (three types) 1

13 6.0 Experimental data A) Table for data of sudden enlargement and sudden contraction. Pipe Q (1/min) h 1 (mm) h (mm) Δh (m) Sudden Enlargement Sudden Contraction 13

14 B) Table for data of different branches (two types) Pipe Q (1/min) h 1 (mm) h (mm) Δh (m) Y Type T Type 14

15 C) Table for data of pipe elbows (three types) Pipe Q (1/min) h 1 (mm) h (mm) Δh (m) 90 angle 90 bend 45 angle 15

16 16

17 7.0 Discussion a) Calculate the loss of coefficient (K) and head loss (n) for each of the flow types; A, B and C as in section 5.0. b) Compare the calculated value with the theoretical value (refer to Fluid Mechanics text book or equation provided in section 3.0) and discuss the possible reasons for different values. c) Discuss the effect of fluid velocity, pipe roughness and pipe diameter on the value of loss coefficient (K) and hence friction loss in pipe. d) Briefly discuss factors contributing to errors or inaccuracy in experimental data and propose recommendation to improve the results. 17

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