1 H16 Losses in Piping Systems The equipment described in this manual is manufactured and distributed by TECQUIPMENT LIMITED Suppliers of technological laboratory equipment designed for teaching. BONSALL STREET, LONG EATON, NOTTINGHAM, NG10 2AN, ENGLAND. Tel: +44 (0) : Fax: +44 (0) General Enquiries: CompuServe, : Internet, Parts & Service: CompuServe, : Internet, Information is available on the Internet at:
2 1. 2. TecQuipment Limited No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system without the express permission of TecQuipment Limited. Exception to this restriction is given to bona fide customers in educational or training establishments in the normal pursuit of their teaching duties. Whilst all due care has been taken to ensure that the contents of this manual are accurate and up to date, errors or omissions may occur from time to time. If any errors are discovered in this manual please inform TecQuipment Ltd. so the problem may be rectified. A Packing Contents List is supplied with the equipment and it is recommended that the contents of the package(s) are carefully checked against the list to ensure that no items are missing, damaged or discarded with the packing materials. In the event that any items are missing or damaged, contact your local TecQuipment agent or TecQuipment directly as soon as possible.
3 SECTION 1.0 INTRODUCTION One of the most common problems in fluid mechanics is the estimation of pressure loss. This apparatus enables pressure loss measurements to be made on several small bore pipe circuit components, typical of those found in central heating installations. This apparatus is designed for use with the TecQuipment Hydraulic Bench H1, although the equipment can equally well be supplied from some other source if required. However, al1 future reference to the bench in this manual refers directly to the TecQuipment bench. 1.1 Description of Apparatus The apparatus, shown diagrammatically in Figure 1.1, consists of two separate hydraulic circuits, one painted dark blue, one painted light blue, each one containing a number of pipe system components. Both circuits are supplied with water from the same hydraulic bench. The components in each of the circuits are as follows: Dark Blue Circuit Light Blue Circuit 1. Gate Valve 2. Standard Elbow Mitre Bend 4. Straight Pipe 5. Globe Valve 6. Sudden Expansion 7. Sudden Contraction 8. ls0mm 90 Radius Bend mm 90 Radius Bend mm 90 Radius Bend
5 Key to Apparatus Arrangement A B C D E F G H J K L Straight Pipe 13.7mm Bore 90 Sharp Bend (Mitre) Proprietary 90 Elbow Gate Valve Sudden Enlargement mrn/26.4mm Sudden Contraction mrn/13.7rnrn Smooth 90 Bend 50mm Radius Smooth 90 Bend 100mrn Radius Smooth 90 Bend ls0mm Radius Globe Valve Straight Pipe 26.4mm Bore In all cases (except the gate and globe valves) the pressure change across each of the components is measured by a pair of pressurized Piezometer tubes. In the case of the valves pressure measurement is made by U-tubes containing mercury.
6 SECTION 2.0 THEORY Figure 2.1 Figure 2.2 Figure 2.3 For an incompressible fluid flowing through a pipe the following equations apply: (Continuity) (Bernoulli) Notation: Q Volumetric flow rate (m 3 /s) V Mean Velocity (m/s) A Cross sectional area (m 3 ) Z Height above datum (m)
7 P Static pressure (N/m 2 ) h L Head Loss (m) ρ Density (kg/m 3 ) g Acceleration due to gravity (9.81m/s 2 ) 2.1 Head Loss The head loss in a pipe circuit falls into two categories: (a) That due to viscous resistance extending throughout the total length of the circuit, and; (b) That due to localized effects such as valves, sudden changes in area of flow, and bends. The overall head loss is a combination of both these categories. Because of mutual interference between neighboring components in a complex circuit the total head loss may differ from that estimated from the losses due to the individual components considered in isolation. Head Loss in Straight Pipes The head loss along a length, L, of straight pipe of constant diameter, d, is given by the expression: where f is a dimensionless constant which is a function of the Reynolds number of the flow and the roughness of the internal surface of the pipe. Head Loss due to Sudden Changes in Area of Flow Sudden Expansion: The head loss at a sudden expansion is given by the expression: ( )
8 Sudden Contraction: The head loss at a sudden contraction is given by the expression: where K is a dimensionless coefficient which depends upon the area ratio as shown in Table 2.1. This table can be found in most good textbooks on fluid mechanics. A 2 /A K Table 2.1 Loss Coefficient For Sudden Contractions Head Loss Due To Bends The head loss due to a bend is given by the expression: where K is a dimensionless coefficient which depends upon the bend radius/pipe radius ratio and the angle of the bend. Note: The loss given by this expression is not the total loss caused by the bend but the excess loss above that which would be caused by a straight pipe equal in length to the length of the pipe axis. See Figure 4.5, which shows a graph of typical loss coefficients. Head Loss due to Valves The head loss due to a valve is given by the expression:
9 where the value of K depends upon the type of valve and the degrees of opening. Table 2.2 gives typical values of loss coefficients for gate and globe valves. Globe Valve, Fully Open 10.0 Gate Valve, Fully Open 0.2 Gate Valve, Half Open 5.6 Table Principles of Pressure Loss Measurements Figure 2.4 Pressurised Piezometer Tubes to Measure Pressure Loss between Two Points at Different Elevations Considering Figure 2.4, apply Bernoulli's equation between points 1 and 2:
10 but: (2-1) therefore ( ) (2-2) Consider Piezometer tubes: ρ [ ( )] (2-3) also (2-4) giving ( ) (2-5) Comparing Equations (2-2) and (2-5) gives (2-6) Principle of Pressure Loss Measurement Considering Figure 2.5, since points 1 and 2 have the same elevation and pipe diameter: ( ) = h L (2-7) Consider the U-tube. Pressure in both limbs of the U-tube is equal at level 00. Therefore equating pressure at 00: ( ) (2-8)
11 Figure 2.5 U- Tube Containing Mercury used to measure Pressure Loss across Valves giving ( ) (2-9) hence: ( ) (2-10) Considering Equations (2-7) and (2-10) and taking the specific gravity of mercury as 13.6: h L = 12.6x (2-11)
12 SECTION 3.0 INSTRUCTIONS FOR USE (1) Connect the hydraulic bench supply to the inlet of the apparatus and direct the outlet hose into the hydraulic bench weighing tank. (2) Close the globe valve, open the gate valve and admit water to the Dark Blue circuit by starting the pump and opening the outlet valve on hydraulic bench. (3) Allow water to flow for two or three minutes. (4) Close the gate valve and manipulate all of the trapped air into the air space in piezometer tubes. Check that the piezometer tubes all indicate zero pressure difference. (5) Open the gate valve and by manipulating the bleed screws on the U- tube fill both-limbs with water ensuring no air remains. (6) Close the gate valve, open the globe valve and repeat the above procedure for the Light Blue circuit. The apparatus is now set up for measurement to be made on the components in either circuit. The-datum position of the piezometer can be adjusted to any desired position either by pumping air into the manifold with the bicycle pump supplied, or by gently allowing air to escape through the manifold valve. Ensure that there are no water locks in these manifolds as these will tend to suppress the head of water recorded and so provide incorrect readings. 3.1 Filling the Mercury Manometer Important: Mercury and its vapors are poisonous and should be treated with great care. Any local regulations regarding the handling and use of mercury should be strictly adhered to.
13 Due to regulations concerning the transport of mercury, TecQuipment Ltd. are unable to supply this item. To fill the mercury manometer, it is recommended that a suitable syringe and catheter tube are used (not supplied) and the mercury acquired locally. If you are wearing any items of gold or silver, remove them. Remove the manometer from the H16 before filling with mercury. The object is to fill the dead-ended limb with a continuous column of mercury and then invert the column so that a vacuum is formed in the closed end of the tube. Hold the manometer upside down and support it firmly. Thread a suitable catheter tube into the manometer tube, ensuring the catheter tube end touches the sealed end of the glass column. Fill a syringe with 10ml of mercury and connect to the catheter tube. Slowly fill the glass column using the syringe, and as the mercury fills the column, withdraw the tube ensuring there are no air bubbles left. Fill up to the bend and return the manometer to its normal position. The optimum level for the mercury is 400mm from the bottom of the U-Tube. When the manometer has the correct amount of mercury in it, a small quantity of water should be poured into the reservoir to cover the mercury and so prevent vapors from escaping into the air. 3.2 Experimental Procedure The following procedure- assumes that pressure loss measurements are to be made on all the circuit components. Fully open the water control valve on the hydraulic bench. With the globe valve closed, fully open the gate valve to obtain maximum flow through the Dark Blue circuit. Record the readings on the piezometer tubes and the U- tube. Collect a sufficient quantity of water in the weighting tank to ensure that the weighing takes place over a minimum period of 60 seconds. Repeat the above procedure for a total of ten different flow rates, obtained by closing the gate valve, equally spaced over the full flow range.
14 With simple mercury in glass thermometer record the water temperature in the sump tank of the bench each time a reading is taken. Close the gate valve, open the globe and repeat the experimental procedure for the Light Blue circuit. Before switching off the pump, close both the globe valve and the gate valve. This procedure prevents air gaining access to the system and so saves time in subsequent setting up..-
15 SECTION 4.0 TYPICAL SET OF RESULTS AND CALCULATIONS 4.1 Results Basic Data Pipe Diameter (internal) Pipe Diameter [between sudden expansion (internal) and contraction] Pipe Material Distance between pressure tappings for straight pipe and bend experiments = 13.7mrn = 26.4mrn Copper Tube = 0.914m Bend Radii 90 Elbow (mitre) 90 Proprietary elbow 90 Smooth bend 90 Smooth bend 90 smooth bend =0 = 12.7mm = 50mm = 100mm = 150mm Identification of Manometer Tubes and Components Manometer Tube Unit Number 1 Proprietary Elbow Bend 2 3 Straight Pipe 4 5 Mitre bend 6 7 Expansion 8 9 Contraction mm bend mm bend mm bend 16
16 4.2 Straight Pipe Loss The object of this experiment is to obtain the following relationships: (a) (b) Head loss as a function of volume flow rate; Friction Factor as a function of Reynolds Number. Test Time To Piezometer Tube Readings (cm) U-Tube Number Collect 18 kg Water (cm) Hg Water (s) Gate-Valve * * Fully Open Water Temperature 23 C Table 4.1 Experimental Results for Dark Blue Circuit Specimen Calculation From Table 4.1, test number 1 Mass flow rate Head loss
17 Volume flow rate (Q) Area of flow (A) Mean Velocity (V) Reynolds Number (Re) For water at 23 C Therefore Re Friction Factor (f) Figure 4.1 shows the head loss - volume flow rate relationship plotted as a graph of log hl against log Q. The graph shows that the relationship is of the form h L α Q n with n = 1.73
18 This value is close to the normally accepted range of 1.75 to 2.00 for turbulent flow. The lower value n is found as in this apparatus, in comparatively smooth pipes at comparatively low Reynolds Number. Figure 4.2 shows the Friction Factor - Reynolds Number relationship plotted as a graph of friction factor against Reynolds Number. The graph also shows for comparison the relationship circulated from Blasius's equation for hydraulically smooth pipes. Blasius's equation: f In the range 104 < Re < 10 5 As would be expected the graph shows that the friction factor for the copper pipe in the apparatus is greater than that predicted for a smooth pipe at the same Reynolds Number. Figure 4.1 Head Loss - Volume Flow Rate
19 5. TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS Figure 4:2 Friction Factor - Reynolds Number 4.3 Sudden Expansion The object of this experiment is to compare the measured head rise across a sudden expansion with the rise calculated on the assumption of: (a) (b) No head loss; Head loss given by the expression: ( )
20 Test Time To Piezometer Tube Readings (cm) V-Tube Number Collect 18 kg Water (cm) Hg Water (s) Globe Valve Table 4.2(a) Experimental Results For Light Blue Circuit Test Time To Piezometer Tube Readings (cm) V-Tube Number Collect 18 kg Water (cm) Hg Water (s) Globe Valve Table 4.2(b) Experimental Results For Light Blue Circuit (continued)
21 Specimen Calculation From Table 4.2 test number 11. Measured head rise = 48mm (a) Assuming no head loss ( ) Since (Bernoulli) [ ( ) ] (Continuity) [ ( ) ] From the table, = 1.67m/s therefore h 2 - h 1 = [ ( ) ] = 0.132m
22 Therefore head rise across the sudden expansion assuming no head loss is 132mm water. (b) Assuming ( ) ( ) (Bernoulli) ( ) ( ) On rearranging and inserting values of d. = 13.7mm and d 2 = 26.4mm, this reduces to which when V 1 = 1.67m/ s gives Therefore head rise across the sudden expansion assuming the simple expression for head loss is 56mm water. Figure 4.3 shows the full set of results for this experiment plotted as a graph of measured head rise against calculated head rise. Comparison with the dashed line on the graph shows clearly that the head rise across the sudden expansion is given more accurately by the assumption of a simple head loss expansion than by the assumption of no head loss.
23 Figure 4.3 Head Rise Across a Sudden Enlargement 4.4 Sudden Contraction The object of this experiment is to compare the measured fall in head across a sudden contraction, with the fall calculated in the assumption of: (a) (b) No head loss; Head loss given by the expression
24 Specimen Calculation From Table 4.2, test number 11. Measured head fall = 221mm water (a) Assuming no head loss Combining Bernoulli's equation and the continuity equation gives: [ ( ) ] Which when V 2 = 1.67m/s gives Therefore head fall across the sudden contraction assuming no head loss is 132mm water. (b) Assuming [ ( ) ] ( ) [ ]
25 From Table 1, when K = giving Which when V 2 = 1.67m/s gives h 1 h 2 = 0.185m _ Therefore head fall across the sudden contraction assuming loss coefficient of is 18.5cm water. Figure 4.4 shows the full set of results for this experiment plotted as a graph of measured head fall against calculated head fall.
26 Calculated decrease in head (cm of water) Figure 4.4 Head Decrease across a Sudden Contraction The graph shows that the actual fall in head is greater than predicted by the accepted value of loss coefficient for this particular area ratio. The actual value of loss coefficient can be obtained as follows: Let h m = measured fall in head and K' = actual loss coefficient then
27 hence which when v 2 = 1.67 m/s gives K' = Bends The aim here is to measure the loss coefficient for five bends. There is some confusion over terminology, which should be noted; there are the total bend losses (K L h L ) and those due solely to bend geometry, ignoring frictional losses (K B, h B ). (Total measured head loss - straight line loss) i. e. i.e. (Head gradient for bend - k x head gradient for straight pipe) Where k = 1 for K B For either, 6. Plotted on Figure 4.5 are experimental results for K B and K L for the 5 types of bends and also some tabulated data for K L. The last was obtained from 'Handbook of Fluid Mechanics' by VL Streeter. It should be noted though, that these results are by no means universally accepted and other sources give different values. Further, the experiment assumes that the head loss is independent of Reynolds Number and this is not exactly correct.
28 Figure 4.5 Graph of Loss Coefficient Is the form of Kg what you would expect? Does putting vanes in an elbow have any effect? Which do you consider more useful to measure, K L or K B?
29 4.6 Valves The object of this experiment is to determine the relationship between loss coefficient and volume flow rate for a globe type valve and a gate type valve. Specimen Calculation Globe Valve From Table 4.2, test number 11. Volume flow rate = (valve fully open) U-tube reading = mercury Therefore h L = = water Velocity (V) = Giving K = = 15.3 Figure 4.6 shows the full set of results for both valves in the form of a graph of loss coefficient against percentage volume flow.
30 Percentage Flow Rate Figure 4.6 Loss Coefficients for Globe and Gate Valves 7.
31 8. TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS Normal manufacturing tolerances assume greater importance when the physical scale is small. This effect may be particularly noticeable in relation to the internal finish of the tube near the pressure tappings. The utmost care is taken during manufacturing to ensure a smooth uninterrupted. Bore of the tube in the region of each pressure tapping, to obtain maximum accuracy of pressure reading. Concerning again all published information relating to pipe systems, the Reynolds Numbers are large, in the region of 1 x 10 5 and above. The maximum Reynolds Number obtained in these experiments, using the hydraulic bench, HI, is 3 x 10 4 although this has not adversely affected the results. However, as previously stated in the introduction to this manual, an alternative source of supply (provided by the customer) could be used if desired, to increase the flow rate. In this case an alternative flow meter would also be necessary. The three factors discussed very briefly above are offered as a guide to explain discrepancies between experimental and published results, since in most cases all three are involved, although much more personal investigation is required by the student to obtain maximum value from using this equipment. In conclusion the general trends and magnitudes obtained give a valuable indication of pressure loss from the various components in the pipe system. The student is therefore given a realistic appreciation of relating experimental to theoretical or published information.
32 SECTION 5.0 GENERAL REVIEWS OF THE EQUIPMENT AND RESULTS An attempt has been made in this apparatus to combine a large number of pipe components into a manageable and compact pipe system and so provide the student user with the maximum scope for investigation. This is made possible by using small bore pipe tubing. However, in practice, so many restrictions, bends and the like may never be encountered in such short pipe lengths. The normally accepted design criteria of placing the downstream pressure tapping pipe diameters away from the obstruction i.e. the 90 bends, has been adhered to. This ensures that this tapping is well away from any disturbances due to the obstruction and in a region where there is normal steady flow conditions. Also sufficient pipe length has been left between each component in the circuit; to obviate any adverse influence neighboring components may tend to have on each other. Any discrepancies between actual experimental and theoretical or published results may be attributed to three main factors: (a) (b) (c) Relatively small physical scale of the pipe work; Relatively small pressure differences in some cases; Low Reynolds Numbers. The relatively small pressure differences, although easily readable, are encountered on the smooth 90 bends and sudden expansion. The results on these components should therefore be taken with most care to obtain maximum accuracy from the equipment. The results obtained however, are quite realistic as can be seen from their comparison with published data, as shown in Figure 4.5. Although there is wide divergence even amongst published data, refer to page 472 of Engineering Fluid Mechanics, it is interesting to note that all curves seem to show a minimum value of the loss coefficient 'K' where the ratio" " is between 2 and 4. It is important to realize and remember throughout the review of the results that all published data have been obtained using much larger bore tubing (76mm and above) and considering each component in isolation and not in a compound circuit.. by Charles Jaeger and published by Blackie and Son L
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