# Flow Through an Orifice[1]

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Flow Through An Oriﬁce: How Oriﬁce Size is Useful in Vacuum Pump Selection Knowledge of the ﬂow through an oriﬁce and oriﬁce size can be used in determining the sizing and selection of a vacuum pump or system. Many of the situations encountered when sizing vacuum equipment, particularly in material handling type applications are resolved with a basic understanding of how ﬂow through an oriﬁce works.To begin the discussion on ﬂow, let’s ﬁrst deﬁne what we mean by the terms oriﬁce and nozzle:  ã An orice can be dened as a round, straight hole having a sharp edge in a plate. ã A nozzle can be dened as a hole with a rounded entrance that transitions into a short, straight section at the throat. For simplicity and the purposes of this discussion, we will refer to both as an oriﬁce. Flow The ﬂow of gas through an orice follows certain “theoretical” formulas. As with any theoretical formula, the exact results achieved may not match perfectly, but they are sufﬁciently close to use in estimating the expected performance requirement.To determine ﬂow (in SCFM) through an oriﬁce, the following equation is used:  Q (ﬂow) = A (area in in2) x V (velocity) There are two types of ﬂow conditions depending on the velocity of the gas; sub-critical and critical ﬂow. For air, when the vacuum level on the pump side of the oriﬁce (i.e. downstream pressure) is less than half of an atmosphere (around 380 Torr), the velocity through the oriﬁce is constantly changing along with the pressure level. In sub-critical ﬂow, the level of SCFM is dependent on the vacuum level – it increases as the pressure decreases (and vice versa).When the downstream pressure reaches half of an atmosphere, the velocity through the oriﬁce becomes ﬁxed (or sonic), and the ﬂow condition changes to critical ﬂow. In critical ﬂow, as the downstream pressure level changes, the ﬂow remains constant as the velocity is ﬁxed. The only way to increase the ﬂow would be to increase the size of the oriﬁce (i.e. area).For all other gases, the critical ratio (rc) can be calculated as follows provided the ratio of speciﬁc heats (k) is known: www.buschusa.com Flow Through An Oriﬁce: Vacuum Pump Selection r  c = = P2 P1 2 k + 1kk - 1 ( )  Flow coefﬁcient  The ﬂow coefﬁcient of an oriﬁce is a relative measure of its efﬁciency. The ﬂow coefﬁcient (C) of a typical sharp-edged oriﬁce is generally accepted to be 0.61 (61% efﬁcient), whereas the ﬂow coefﬁcient of a typical nozzle is generally accepted as 0.97 (97% efﬁcient).Note that the presence of dirt or burrs on the oriﬁce can signiﬁcantly affect the efﬁciency, and hence ﬂow capacity of the oriﬁce. Figure 1 below illustrates this effect: www.buschusa.com Flow Through An Oriﬁce: Vacuum Pump Selection OriﬁceC = .61NozzleC = .97C > .61C < .61 Figure 1 Flow thru an Oriﬁce When sizing vacuum pumps or vacuum systems that utilize an oriﬁce, nozzle, slot, hole, etc., an oriﬁce chart can be used to help estimate airﬂow (SCFM) as shown in Figure 2. For slots, equating the slot area in square inches to the area in square inches of an oriﬁce is used to determine the oriﬁce equivalent.   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-303/64  0.0017 0.115 0.181 0.220 0.246 0.270 0.291 0.312 0.329 0.344 0.352 0.360 0.366 0.370 0.371 0.372 1/16  0.0031 0.212 0.321 0.386 0.439 0.483 0.523 0.559 0.591 0.615 0.633 0.645 0.658 0.661 0.663 0.667 5/64  0.0048 0.338 0.494 0.620 0.701 0.774 0.831 0.873 0.908 0.950 0.978 1.00 1.02 1.03 1.04 1.04 3/32  0.0069 0.483 0.718 0.881 1.01 1.12 1.20 1.26 1.33 1.38 1.41 1.45 1.48 1.50 1.51 1.51 7/64  0.0094 0.666 0.989 1.21 1.39 1.53 1.65 1.75 1.82 1.89 1.94 1.99 2.02 2.05 2.06 2.06 1/8  0.0123 0.869 1.33 1.60 1.84 2.04 2.18 2.30 2.40 2.48 2.55 2.59 2.65 2.67 2.70 2.71 9/64  0.0155 1.10 1.63 2.01 2.30 2.53 2.72 2.86 2.97 3.09 3.18 3.25 3.31 3.36 3.39 3.42 5/32  0.0192 1.35 2.00 2.47 2.81 3.10 3.31 3.50 3.66 3.81 3.93 4.03 4.10 4.16 4.18 4.20 11/64  0.0232 1.59 2.38 2.92 3.38 3.75 4.04 4.25 4.43 4.58 4.73 4.84 4.94 5.02 5.09 5.13 3/16  0.0276 1.88 2.85 3.51 3.99 4.37 4.68 4.94 5.16 5.35 5.56 5.72 5.87 5.94 6.05 6.10 13/64  0.0324 2.22 3.27 4.00 4.57 5.08 5.50 5.82 6.08 6.31 6.51 6.70 6.86 6.99 7.07 7.14 7/32  0.0376 2.61 3.73 4.59 5.28 5.87 6.32 6.66 7.00 7.27 7.52 7.75 7.91 8.06 8.17 8.26 15/64  0.0431 3.00 4.25 5.22 6.02 6.66 7.24 7.66 7.99 8.32 8.59 8.82 9.04 9.22 9.36 9.48 1/4  0.0491 3.38 4.76 5.89 6.80 7.54 8.15 8.66 9.05 9.40 9.72 10.02 10.24 10.46 10.61 10.75 9/32  0.0621 4.16 5.97 7.29 8.32 9.25 9.99 10.72 11.20 11.74 12.11 12.58 12.93 13.23 13.35 13.62 5/16  0.0767 5.12 7.28 8.73 9.96 11.07 11.99 12.79 13.48 14.05 14.64 15.17 15.69 16.06 16.44 16.83 11/32  0.0928 5.90 8.68 10.52 12.12 13.40 14.39 15.32 16.11 16.92 17.57 18.27 18.80 19.34 19.74 20.19 3/8  0.1104 6.86 10.17 12.59 14.46 16.07 17.26 18.30 19.19 20.20 20.90 21.68 22.45 23.18 23.67 24.35 13/32  0.1296 8.41 12.22 14.84 17.06 18.82 20.30 21.60 22.71 23.77 24.70 25.61 26.41 27.08 27.88 28.90 7/16  0.1503 9.96 14.55 17.54 19.92 22.07 23.82 25.27 26.66 27.75 28.76 29.72 30.66 31.72 32.35 33.54 15/32  0.1726 11.40 16.61 20.33 23.04 25.23 27.34 29.10 30.62 31.88 32.95 34.14 35.21 36.19 37.03 38.37 1/2  0.1963 13.04 19.03 23.30 26.42 28.90 30.93 32.78 34.65 36.21 37.61 38.82 39.94 40.82 41.87 43.38 9/16  0.2485 17.59 25.00 30.32 34.39 37.72 40.53 43.12 45.20 47.12 48.73 50.20 51.50 52.47 53.90 55.08 3/4  0.4418 31.27 44.44 53.90 61.14 67.06 72.05 76.66 80.36 83.77 86.63 89.24 91.56 93.28 95.82 97.92 1  0.7854 55.59 79.01 95.83 108.69 119.21 128.09 136.28 142.85 148.92 154.01 158.66 162.77 165.83 170.35 174.08 1 1/2  1.7671 125.08 177.78 215.61 244.55 268.23 288.21 306.63 321.42 335.08 346.52 356.98 366.22 373.12 383.29 391.68 2  3.1416 222.37 316.05 383.30 434.76 476.86 512.38 545.12 571.42 595.69 616.04 634.63 651.06 663.32 681.40 696.32 2 1/2  4.9087 347.46 493.83 598.91 679.31 745.09 800.59 851.75 892.84 930.77 962.57 991.60 1017.28 1036.44 1064.69 1088.00 3  7.0686 500.34 711.11 862.44 978.20 1072.92 1152.85 1226.52 1285.69 1340.30 1386.10 1427.91 1464.89 1492.48 1533.16 1566.72 3 1/2  9.6211 681.02 967.90 1173.87 1331.44 1460.37 1569.16 1669.44 1749.97 1824.30 1886.63 1943.55 1993.88 2031.43 2086.80 2132.48 4  12.5664 889.49 1264.20 1533.22 1739.03 1907.42 2049.52 2180.49 2285.67 2382.76 2464.17 2538.51 2604.25 2653.30 2725.61 2785.28 Inches HgvAreain²OrificeDiameter  Flow (SCFM) through a Square Edge Oriﬁce Flow Coefﬁcient = .61 Figure 2  www.buschusa.com Flow Through An Oriﬁce: Vacuum Pump Selection Oriﬁce Ratios For most applications that use vacuum, multiple orices are used. A high speed cartoning machine for example will typically use one or more sets of suction cups that grip or hold the box through the set up and unloading stages and where each cup uses an inner oriﬁce through which the air is removed (or evacuated) by the vacuum system.In multiple oriﬁce situations the sizing of the connecting lines or manifolds is key to the speed at which the air is removed and hence the machine/system efﬁciency. Often, incorrect manifolding of the oriﬁces is witnessed. By introducing the concept of oriﬁce ratios we can better assist the customer, be it an OEM or an end user.The term oriﬁce ratio refers to the size of the area upstream on the oriﬁce (towards the point of use) to the area downstream. As an example, consider a typical situation where four suction cups are used on a common arm or end effector, with each cup having an internal ¼” id oriﬁce. It is not unusual that these cups would then be manifolded together into a common line, then to a single control valve that turns the vacuum on/off through the cycle. In this example, let’s assume that the four cups are connected to a common ¼” line, then to a ¼” control valve. The below chart in Figure 3 provides the area for some of the common size oriﬁces in sizes up to 6”. 3/64 0.0017 15/64 0.0431 1 0.78541/16 0.0031 1/4 0.0491 1 1/2 1.76715/64 0.0048 9/32 0.0621 2 3.14163/32 0.0069 5/16 0.0767 2 1/2 4.90877/64 0.0094 11/32 0.0928 3 7.06861/8 0.0123 3/8 0.1104 3 1/2 9.62119/64 0.0155 13/32 0.1296 4 12.56645/32 0.0192 7/16 0.1503 4 1/2 15.904311/64 0.0232 15/32 0.1726 5 19.63503/16 0.0276 1/2 0.1963 5 1/2 23.758313/64 0.0324 9/16 0.2485 6 28.27437/32 0.0376 3/4 0.4418 6 1/2 33.1831 OrificeDiameter Areain²OrificeDiameter Areain²OrificeDiameter Areain² Area Chart Figure 3 As shown in the table above, a ¼” id orice has an area of .0491 in2. As we are using four in this example, we add the areas together to get a combined total area of .20 in2. In connecting the four together via the ¼” line, we now have a situation where the total oriﬁce area in use is greater than the connected line area resulting in a “pinch point” in the system. Oriﬁce ratios where the upstream area is greater than the downstream area result in situation likened to a vacuum rush hour trafﬁc backup. Due to the pinch point, the air cannot be evacuated through the connected line as quickly as necessary so the evacuation to the desired pressure level is delayed.  In the curve set below in Figure 4, we represent the time it takes for the pressure levels on both sides of the orice to equalize in a typical 4:1 orice ratio situation (note that it takes almost 2 full seconds for the pressure to equalize). Eventually, the pressure drop is overcome and the levels will be the same, but at the expense of time. www.buschusa.com Flow Through An Oriﬁce: Vacuum Pump Selection 4 : 1 Orice Ratio Figure 4A better solution is to manifold the cups to a connected line that has at least the same area as the total oriﬁce area. In this example, using a ½” line to manifold the cups and a minimum ½” control valve (which should always be at least the same size or larger as the connecting line) changes the oriﬁce ratio to 1:1.By working to maintain a 1:1 oriﬁce ratio, the time it takes the pressure levels to equalize is greatly reduced and as a result, the vacuum level in the cup reaches the required level faster so that the machine can also run faster. This is represented in the curve set in Figure 5 below:

Jul 23, 2017

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