Rutenbeck; GLR Pressure Drop

Group Leader Report Julianne Rutenbeck CHEN 3130-‐004 Dr. Wendy Young 02/10/2015

2

Table of Contents Objectives ….……………………………………………………………………………………………………………… 3 Apparatus and Equipment …………………………………………………………………………………………. 4

Process Flow Diagram ………………………..…………………………………………………………………. 4 Operating Instructions ………………………………………………………………………………………………. 5

Start up ………….……………………………………………………………………………………………………. 5 Calibrations ………………………………………………………………………………………………...................... 5 Data Collection ………………………..…………………………………………………………………..................... 6 Shut Down …………………………………………………………………………………………………………... 6 Safety ………………………………………………………………………………………………………………….. 6

Calculations ………………………………………………………………………………………………….................... 7 Calculation Flowcharts …..……………………………………………………………………………………… 7

Error Analysis …………………………………………………………………………………………………………… 9 Bibliography …………………………………………………………………………………………………………... 10 Appendices ……………………………………………………………………………………………………………... 11

Appendix I: Table of Nomenclature and Physical Properties ……………………………………... 11 Appendix II: Instrument Specifications ……………………………………………………………............ 12 Appendix III: Specified flow rates to be studied………………………………………………………….. 12 Appendix IV: Pipe Specifications ……………………………………………………………………………….. 13 Appendix V: Example Moody Diagram ……………………………………………………………………... 14

3

Objectives This experiment will investigate how physical parameters affect the pressure drop

in pipes. The pressure drop in straight pipes over a given length will be measured for various pipe diameters and volumetric flow rates. With these data, an experimental moody chart will be created and compared to typical versions. A typical moody chart plots the Reynolds number – a dimensionless parameter used to characterize fluid flow – versus the friction factor, at various values of the relative roughness (ϵ/D), which is characteristic of the piping material (Refer to Appendix V for an example Moody chart). The plot created from this experiment will have only one value of the roughness factor and therefore the relative roughness will depend only on the pipe diameter. The Reynolds number and friction factor can both be calculated from properties of the fluid and knowledge of the flow rate, pipe diameter, and the pressure change over a given length of tube (equations 5, 8; see Calculations, Flow Chart II, pg. 8). Flow rate and diameter will be varied and the pressure drop for each combination will be recorded.

Pressure changes through a number of flow components will also be observed. Similar to the method used for straight pipes, the pressure drop around the components will be measured as a function of flow rate. These components consist of a ball valve (H), a bonnet valve (G), a 90o bend (K), a venturi meter (I), and an orifice meter (J, see Figure 1, pg. 4). Once the data have been obtained, a plot will be created for each of the two valves and the bend, showing equivalent length versus the Reynolds number. The equivalent length is an effective distance, equivalent to the length of straight pipe that would cause the same change in pressure at the given flow rate and diameter; it can be calculated from these three parameters (equation 10, Calculation Flow Chart III, pg. 9). The venturi and orifice meters will each be analyzed with a plot of the discharge coefficient versus the Reynolds number at various flow rate and diameter values. The discharge coefficient is a dimensionless parameter used to describe the relative efficiency of a valve discharging to a reservoir (equation 11, Calculation Flow Chart IV, pg. 9). By the end of the experiment, the dependence of the pressure drop on diameter and flow rate will be approximately known. The resulting correlations and relationships may be used in the future to help design a new piping network with this piping material.

4

Apparatus and Equipment

Figure 1. Process Flow Diagram.

Orifice MeterVenturi Meter

Air release valvesBonnet Valve

Ball ValvePressure Gauge/Transducer Connection

Gate valve

Rotameter switch valve

Rotameter

Flow inFlow out

Line 6

Line 5

Line 4

Line 3

Line 2

Line 1

Reservoir

PumpA

B

CD

E

F

G H

I J

2 psid pressure transducer



L

K

Entrance length L=length of P dropExit Length

M

5

Apparatus & Equipment The Process Flow

The pump pushes water up from the reservoir, through one of the rotameters (M), and up the left side of the apparatus. The air release valves (F), allow the water to air push up and out of the system. Each line has a ball valve that controls the flow into that tube. Lines one, four, five, and six are just straight pipes with pressure sensor ports on opposite ends. Line two has the Venturi meter (I), the orifice meter (J), and the bend (K). Line three has two different kinds of valves – Ball (H) and Bonnet (G). Each of these components has pressure sensor ports on either side of them. The water flows out on the opposite side of the apparatus, passes through the gate valve (L), and drains back into the reservoir to be recycled.

Table 1. Process Flow Diagram Components

Component G Bonnet valve A Pump H Ball valve B Valve to switch rotameters; Orifice 0.01905 m I Venturi Meter C Ball valve to open each line J Orifice Meter D Pressure sensor connection port K Bend E Brass Alloy 260 Tubing L Gate valve F Air release valves M Rotameter

Operating Instructions and Safety Start Up Before engaging the pump and beginning data collection, the apparatus must be in the proper state. One of the rotameter valves should be open and the other closed (B; see figure 1, pg. 4); if both are in the same position, damage to the pump may occur. The entry valves to each pipe should be such that the lines’ under study are open and the rest are closed (C). On the exiting side, the gate valve leading into the drain tub (L) should be all the way open and secured to the reservoir. Once the water has established full flow and the experiment begun, the exit valve may be adjusted accordingly to avoid vacuum pressures. When all of this has been accomplished, the pump is ready to be engaged. When the pump is started, the lines must be cleared of air to avoid hammering and equipment damage. To clear the line, open the air release valves on each side of the apparatus (F). When water can be seen in the tube, all the air has been cleared from the lines and the valve can be shut. Calibration The rotameters (M) will be calibrated with a catch and weigh. Once full flow has been established – the ¾” lines may take several minutes – the process can begin. The information being recorded will be the time for which water is allowed to flow into the bucket, along with the mass of the bucket, before and after the water is allowed to drain into it. With this information, equation (1) can be used to calculate the actual flow rate and compare it to the rotameter reading. For each rotameter, five different flow rates will be measured, and three replicates will be performed at each level. This data should then be

6

consolidated into a calibration curve, which then can be used for the duration of the experiment. Table 5 in appendix III shows the specified levels to be calibrated. At each of the flow rates, the pressure transducers will also be calibrated. Using the same gauge, measurements will be taken across the pipe at the same sites that the transducers connect to. Since there are two rotameters and two pressure transducers that require calibration, the ten-‐psid transducer will be calibrated with the 0.2-‐2 gpm rotameter, and the five-‐psid transducer with the 2-‐15 gpm rotameter. The gauge and transducer data will be compared in a calibration curve. Between each replicate of the calibrations, the flow rate should be varied slightly and brought back to the original level. Data Collection Since the aim of this experiment is to explore a wide range of Reynolds numbers and pressure changes, a wide variety flow rates will be investigated. For each straight tube, four flow rates have been specified and three replicates will be performed at each. If time does not permit for this many trials, one flow rate for each line has been specified as being less necessary; table 6 (appendix III) shows the specified flow rates to be studied. At each specified flow rate, the actual flow reading and pressure drop across the appropriate transducer will be recorded. Pressure drop will be measured via LabView Software. The experiment will generate between thirty-‐six and forty-‐eight data points. These will be used to create an experimental moody chart (see calculations flow chart II for more information). The generated plot will be compared to typical ones found in literature. An example Moody chart has been attached in Appendix V for comparison with the results obtained. Since all the lines will be used, when switching between them, one must open the next valve before closing the current one. If all entry valves are closed, damage to the equipment may result. After the straight pipe data have been taken, lines two and three will be studied. Again, flow rate and pressure drop around each component will be varied and recorded. These data will be used to make two more plots – discharge coefficient (calculation flow chart IV) versus Reynolds number for the venturi and orifice meters and equivalent length (calculation flow chart III) versus Reynolds number for the valves and bend. Shut Down To shut down the apparatus, simply turn off the pump. After this, shut all the gate valves to the lines and all other valves should be in safe positions for future use. Because water may leak from the lines or reservoir, dry the surrounding area for the safety of others in the lab. Safety

• As stated above, water leakage increases the risk of slipping in the lab. • The pump is an electrical component in a water reservoir. Be careful not to allow

loose wires, or other conductors that have electricity running through them, to come into contact with the water.

7

Calculations -‐Refer to Appendix I for variable definitions and physical property values.

I. Calibration of Rotameter

II. Experimental Moody Chart

Catch & Weigh

• Measure mass of empty bucket. • Time how long water llows into the bucket. • Measure the mass of the bucket and water(m).

Obtain Flow Rates

• Q=(m/t)(1/ρ) (1)

• Record observed llow rate from rotameter.

Callibration Curve

• Plot Q vs. the readings from the rotameter.

Velocity •  ν=Q/A (2)

Pipe properties

• A=π(D/2)2 (3) • Relative Roughness = ϵ/D (4)

Reynolds Number

• Re=ρνD/μ (5) • τw= -‐(dP/dz)(D/4) (6)

Friction Factor

•  ff=2τw/ρν2 (7) • Assuming the shear stress is constant. •  ff = (ΔP)D/2ρν2L = (P1-‐P2)D/2ρν2L (8)

Moody Chart

• Plot ff vs. Re for different experimental values of ν, ΔP/L, and D. Compare this with charts found in literature.

8

Assume

• Horizontal llow • Uniform velocity prolile upstream and downstream

Discharge Coeflicient

Reynolds Number

• Re=ρνD/μ (4)

Graph

• Plot Cd vs. Re for each meter at various llow rates. Analyze the graphs.

III. Bend and Valves

IV. Venturi meter and Orifice meter

𝐶! =!!!!!!

!(!!(!!!!)!)

! !" 11

Reynolds Number

• Re=ρνD/μ (4) • Use this along with the experimental moody chart to get ff

Loss Coeflicient

• Assuming fully-‐developed, steady, incompressible llow. • KL = 2Ploss/ρν2 = 2(P1-‐P2)/ρν2 (9)

Equivalent Length

•  leq=KLD/ff (10) • Graph leq vs. Re for the bend and both valves at various values of ΔP, ff, and ν.

9

Error Propagation Three replicates will be done for each measurement. The data taken from these measurements will be analyzed with the equations and graphs mentioned previously. The error associated with the measurements will propagate when these calculations are performed, so the equations below should be used to estimate the error associated with a calculated value.

𝛿𝑄 =1𝜌𝑡

!

(𝛿𝑚)! + (−𝑚𝜌𝑡!)

!(𝛿𝑡)! (1)

𝛿𝑉 =𝛿𝑄𝐴 (2)

𝛿𝑓! =𝐷

2𝜌𝑣!𝐿

!

𝛿Δ𝑃 ! + (−Δ𝑃𝐷𝜌𝑣!𝐿 )

! 𝛿𝑣 ! (8)

𝛿𝐾! =2𝜌𝑣!

!

(𝛿Δ𝑃)! +−4Δ𝑃𝜌𝑣!

!

(𝛿𝑣)! (9)

𝛿𝑙!" =𝐷𝑓!

!

𝛿𝐾! ! + (−𝐷𝐾!𝑓!!

)!(𝛿𝑓!)! (10)

𝛿𝐶! =4𝜋𝐷!!

𝜌(1− (𝐷!𝐷!)!)

2 𝛥𝑃

!

(𝛿𝑄)! +−2𝑄𝜋𝐷!!

𝜌(1− (𝐷!𝐷!)!)

2(Δ𝑃)!

!

(𝛿Δ𝑃)! (11)

The equations for which these errors should be used are noted on the right of the

equation. The error for each measurement will be the greater of two errors: the error associated with reading the measurement and random error between measurements due to random fluctuations (standard deviation). The error associated with equation one should not be used as the error value in the latter equations; it is only for the catch and weigh. Manufacturer data are shown in appendix II, table 4. The precision is an estimate based on the markings on the instrument. No measurements were taken with them in order to verify the estimates. The systematic error for measurements of volumetric flow rate and pressure drop should be eliminated with the calibration of the instruments.

10

Bibliography Kestin, J., Sokolov, M., Wakeham, W. A. (1978). Viscosity of Liquid Water in the Range -‐8oC

to 150oC. J. Phys. Chemical Reference Data, Vol. 7. Retrieved from: http://www.nist.gov/data/PDFfiles/jpcrd121.pdf

The Engineering Page. Retrieved from: http://www.the-‐engineering-‐page.com/forms/dp/typ_eps.html

The Engineering Toolbox. Retrieved from: http://www.engineeringtoolbox.com/moody-‐diagram-‐d_618.html

11

Appendices Appendix I

Table 2. Table of Nomenclature. Symbol Definition Units Obtained by:

Q Volume flow rate m3/s Calculated/measured m Mass of water kg Measured ρ Density of water @ Twater ≅ 25oC kg/m3 Constant (varies with T) t time s Measured T Temperature of water oC Measured (LabView) τw Shear stress at the wall N/m2 Calculated A Cross sectional area of pipe m2 Calculated D Diameter of pipe in Constant ν Velocity m/s Calculated ff Fanning friction factor -‐-‐ Calculated ΔP Differential pressure psid Measured (LabView) P1 Upstream pressure psig Measured P2 Downstream pressure psig Measured L Length of pipe between P1 & P2 in Constant Re Reynolds number -‐-‐ Calculated μ Dynamic viscocity of water at 25oC Ns/m2 Constant (varies with T) D1 Large diameter of venturi/orifice meter in Constant D2 Small diameter of venturi/orifice meter in Constant Cd Discharge Coefficient -‐-‐ Calculated KL Loss Coefficient -‐-‐ Calculated leq Equivalent length of straight pipe m Calculated ϵ Roughness Factor m Constant

Table 3. Table of Physical Properties. Property Value Units 1ρ (at 25oC) 997.1 kg/m3

1μ (at 25oC) 8.902E-‐4 Ns/m2

2ϵ (Brass) 1.0E-‐7–1.5E-‐7 m 1-‐ Kestin et al., 1978 2-‐ “The Engineering Page”

12

Appendix II Table 4. Instrument Specifications

Instrument Mfr.1 Range Units 3Accuracy/Bias Precision Tolerance Pressure Gauge

WIKA 0-‐15 psig ± 2.5% ±0.5 If the same gauge is used to measure pressure in both positions, the bias should be

eliminated Pressure Gauge

WIKA 0-‐30 psig ± 2.5% ±1.0

Pressure Transducer

Dwyer 0-‐2 psid ± .25% ±0.02 The transducers can be

calibrated using the gauges to measure P1 and P2

Pressure Transducer

Dwyer 0-‐5 psid ± .25% ±0.02

Pressure Transducer

Dwyer 0-‐10 psid ± .25% ±0.02

Rotameter King 0.2-‐2 gpm ± 5% ± 0.5 The rotameters will be calibrated Rotameter King 1.5-‐15 gpm ± 5% ± 0.5

____________________________________ 1-‐Manufacturer 2-‐The data are collected using Labview software. 3-‐Estimates based on multiple possible models

Appendix III

Table 5. Calibration flow rate specifications Rotameter Flow rates to be calibrated (gpm) 0.2-‐2 gpm 0.35 0.8 1.2 1.6 2.0 2-‐15 gpm 2.1 4.3 6.5 8.7 11

Table 6. Data collection flow rates

Flow Rates to be studied (gpm) Possible flow rates

Line 1 4 5.2 8 11 gpm Line 4 3 4.5 8.5 5.3 gpm Line 5 0.8 1 4.5 1.85 gpm Line 6 0.35 0.5 1.3 0.9 gpm

13

Appendix IV Table 7. Straight Tube Specifications and Recommendations. Line 1 Line 4 Line 5 Line6

I.D. (m) 0.015748 0.0110744 7.8994E-‐3 4.7244E-‐3 Recommended Gauge 15 psig 15 psig 30 psig 30 psig

Recommended Transducer 5 psid 5 psid 10 psid 10 psid Recommended Flow Rate

(m3/s)*104 6.94–2.52 5.36–1.89 2.84–0.505 0.82–0.221

Length between psid measurements (m)

1.0922 1.09855 1.09855 1.09855

Entry Ball Valve Orifice (m) 0.019304 0.0103124 7.1374E-‐3 4.7498E-‐3 Relative Roughness (x105) 0.64–0.95 0.9–1.35 1.27–1.9 2.12–3.18

Table 8. Component Specifications and Recommendations. Venturi

Meter Orifice Meter

Bonnet Valve

Ball Valve

Line 2 2 3 3 Length 0.0889 m n/a n/a n/a Throat 1L 0.022225 m n/a n/a n/a

Throat/Bore Diameter

9.525E-‐3 m 0.014732 m

n/a n/a

1L across 0.4572 m 0.34925 m 0.34925 m 0.3556 m 1L upstream .22225 m 0.18415 m n/a n/a

1L down-‐stream .23495 m 0.1651 m n/a n/a Entry valve orifice (m)

0.019304 -‐-‐ 0.0103124 -‐-‐

2Flow Rate*104 5.68–2.52 m3/s 4.1–1.89 m3/s -‐-‐ -‐-‐ 2P Gauge 15 psig 15 psig 30 psig 30 psig

2Transducer 5 psid 5 psid 10 psid 10 psid

14

Appendix V

Figure 2. Example experimental Moody Chart (The Engineering Toolbox).

Rutenbeck; GLR Pressure Drop

Documents

Transcript of Rutenbeck; GLR Pressure Drop