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W
ould you like to make aquick mental calculationto determine approximateflowrate, velocity, or pipe
and duct sizes for many commonsituations? This article presentstwo methods for estimating flowcharacteristics without the aid ofcharts, tables, calculators or soft-ware programs. One method appliesto liquid flow in pipes, and the otherto air flow in ducts. The techniquesare intended to be simple enoughto yield useful answers withina few seconds.
Liquid flow in pipes
Sizing pipes for liquid transportnearly always requires an engi-neer to seek a preferred velocity toestablish favorable flow character-istics. This calculation techniqueallows an engineer to estimate ve-locity, flowrate and pipe diameterrelationships when reference datais unavailable. The technique firstestablishes a flowrate (Q, in gpm)corresponding to a velocity of 10 ft/sin a Schedule 40 pipe with diameter D (inches). That information can
then be extrapolated for flow prop-erties at other conditions. Equation(1) applies to the flow of liquidsthrough pipes.
Q10 = D2 × 25 (1)
Consider the following examples,which employ Equation (1) to quicklyapproximate pipe velocity.
Example 1. What flowrate will yielda velocity of 8 ft/s in a 2-in. pipe?First, mentally calculate the follow-ing using Equation (1): Q
10
= 22 ×25 = 100 gpm. This means that 100gpm will flow in the 2-in. pipe at 10ft/s. We want to determine the flow-
rate in the same pipe at 8 ft/s. Weknow that 8 ft/s is 80% of 10 ft/s, sosimilarly, 80% of 100 gpm is 80 gpm.Literature shows the velocity of 80gpm in a 2-in. Schedule 40 pipe is7.65 ft/s. Our estimate is within 5%of the literature value.
Example 2. What is the veloc-ity of 2,500 gpm flowing in a 12-in.pipe? Again, we use Equation (1) tomentally calculate the flow at thereference velocity of 10 ft/s: Q10 =122 × 25 = 3,600 gpm flowrate at
10 ft/s. To determine the velocity at2,500 gpm, we start with the factthat 2,500 is roughly 70% of 3,600.70% of 10 ft/s is 7 ft/s. Literatureshows the velocity of 2,500 gpm ina 12-in. Schedule 40 pipe is 7.17 ft/s.Our estimate is within 3% of theliterature value.
Each problem is solved in twobasic steps. The first is to multiplythe square of the pipe diameter by25. The second step is to determinethe ratio of the target flow to the
flow yielding 10 ft/s to arrive atthe desired conditions. In a man-ner similar to the examples above,pipe diameters can be derived fromflow and velocity data. That calcu-lation is performed by assuming apipe diameter, calculating its flowat 10 ft/s, comparing its flow prop-erties at desired flow or velocity,and iterating to another diameterif necessary.
This technique is not exact, butit gives the engineer relatively ac-curate results very quickly. WhileEquation (1) is intended for Sched-ule 40 pipes, and accuracies for pipes
with varying wall thicknesses willbe slightly different, this calculationmethod will quickly yield a close es-timation. Figure 1 displays how cal-culated values compare to literature values. The error between estimated values and actual values should beaccurate enough for initial sizing es-timates. However, accuracy is dimin-ished significantly for pipes with adiameter of less than one inch.
Air flow in ducts
The technique used for liquids inpipes can be applied to air in ductsat standard (atmospheric) pressureand temperature. Equation (2) ap-plies to air flowing at these condi-tions, using a reference air velocityof 2,000 ft/min.
Q2000 = D2 × 11 (2)
Consider the following examples,which employ Equation (2) to evalu-ate flowrate (Q, in ft3 /min) in sheet-metal air ducts.
Example 3. What flowrate willyield a velocity of 3,000 ft/min in a10-in. duct? We must first use Equa-tion (2) to mentally calculate thefollowing: Q2000 = 102 × 11 = 1,100ft3 /min, which is the flowrate yield-ing an air velocity of 2,000 ft/min.We want to determine the flowratethat results in a velocity of 3,000 ft/ min. 3,000 ft/min is 150% of 2,000ft/min. Therefore, 150% of 1,100ft3 /min = 1,650 ft3 /min. A checkagainst the literature values showsthat the velocity of 1,650 ft3 /minin a 10-in. galvanized sheet-metalduct is 3,100 ft/min. Our mental
Feature Report
42 CHEMICAL ENGINEERING WWW.CHE.COM FEBRUARY 2014
Feature Report
Simple calculation methods for estimating
flow characteristics in pipes and ducts
save engineers’ time
Quick Pipe and Duct
Flow Calculations
Part 2
Bruce R. Smith
Sidock Group
7/26/2019 feb14_MPB2
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calculation is within 3.2% of theliterature value.
Example 4. What is the velocitythat corresponds to a flowrate of6,000 ft3 /min in a 20-in. duct? First,of course, we must mentally calcu-late the flowrate corresponding tothe reference velocity of 2,000 ft/ min: Q2000 = 202 × 11 = 4,400 ft3 / min. Now, we can solve for the ve-locity which corresponds to 6,000ft3 /min flow in the pipe — 6,000 is
slightly less than 150% of 4,400,and 150% of 2,000 ft/min is 3,000 ft/ min. Literature shows the velocity of6,000 ft3 /min in a 20-in. sheet-metalduct is 2,800 ft/min. Our estimateis 7% greater than the literature value, but a value somewhat greaterthan the actual was expected whenwe rounded to 150%.
This technique is accurate towithin 1% if exact numbers arecalculated for the flowrate percent-ages. As seen in Examples 3 and 4,
accuracy diminishes if estimates arenot exact. While this technique is
intended for use with sheet-metalducts, accuracies for ducts with varying wall thicknesses will not besignificantly different. Figure 2 com-pares these calculations to literature values. The two lines are practicallyidentical when calculations are pre-
cise, rather than rough estimates.In conclusion, when rough initial
estimates are needed, engineers canconfidently apply these simple, time-saving methods to characterize flowin pipes and ducts. ■
Edited by Mary Page Bailey
CHEMICAL ENGINEERING WWW.CHE.COM FEBRUARY 2014 43
0
5,000
10,000
15,000
20,000
25,000
0 5 10 15 20 25 30
Q 1 0
( f l o w r a t e a t 1 0 f t / s v e l o c i t y , g p m )
Pipe diameter, inches(standard wall thickness, Sch. 40 pipe)
Literature values
Estimated values
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
0 5 10 15 20 25 30
Q 2 0 0 0
( f l o w r a t e a t 2 , 0 0 0
f t / m i n v e l o c i t y ,
f t 3 / m i n )
Duct diameter, inches (sheet-metal)
Calculated values
Literature values
FIGURE 1. A comparison of literature values with calculatedvalues shows that these quick, simplified pipe-flow calcula-tions are accurate enough for initial sizing estimates
FIGURE 2. The rough estimates resulting from the duct-flowcalculation method are extremely close to literature values forairflow in sheet-metal ducts
AuthorBruce Smith is a projectmanager at Sidock Group,Inc. (379 W. Western Ave.,Muskegon, Mich. 49441;Phone: 231-722-4900; Email:[email protected]).Previously, he was employedas a senior research engineerat The Dow Chemical Co.after working as an engineerin the automotive and miningindustries. He has experience
with a wide variety of technologies and is a reg-istered professional engineer in multiple states.Smith is credited with several patents and tech-nical articles. He holds a B.S.Ch.E. from Michi-gan Technological University.
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