TankExampleNov2016. Table of contents. Layout
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1 Table of contents Task... 2 Calculation of heat loss of storage tanks... 3 Properties ambient air Properties of air... 7 Heat transfer outside, roof Heat transfer in flow past a plane wall... 8 Properties tank medium Properties of heavy fuel oils... 9 Inside heat transfer coefficient, bottom Heat transfer by natural convection around immersed bodies Gas properties Properties of air Heat transfer outside, shell Heat loss of walls and pipeworks Inside heat transfer coefficient, wet shell Heat transfer by natural convection around immersed bodies Inside heat transfer coefficient, dry shell Heat transfer by natural convection around immersed bodies Inside heat transfer coefficient, roof Heat transfer by free convection in enclosed fluid layers Physical properties of heating medium Properties of thermal oils Tube-side heat transfer Heat transfer in pipe flow Heat transfer coil around tubes Heat transfer by natural convection around immersed bodies Pressure drop in coil Pressure drop in flow through pipes Layout Input values: or Calculated values: or Critical values: or Estimated values: or Lauterbach Verfahrenstechnik GmbH
2 Task Heavy fuel oil HFO 180 shall be stored in a storage tank with circular cross section at a minimum temperature of 50 C. Dimensions of the tank: inside diameter: 12 m Height: 15 m Filling level: 14 m The shell of the tank consists of 8 mm steel (St steel λ = 52 W/(m K)) and is insulated shell side and roof side with 100 mm mineral wool (λ = 0,04 W/(m K)). It is placed on a 250 mm thick concrete plate with λ = 2,5 W/(m K). What is the heat loss of the tank in the winter at an air temperature and ground temperature of - 20 C and a wind velocity of 10 m/s? For compensating the heat losses the tank is heated with a flat coil. The heat transfer takes place by free convection. Heating medium: Thermal oil Transcal LT Volume Flow: 10 m³/h Inlet temperature: 140 C Flat coil: DN 50 (60.3 x 2.9 mm) Material: Steel Thermal conductivity 52 W/(m K) A possible fouling of the coil is not considered. What is the heat transfer area? Lauterbach Verfahrenstechnik GmbH
3 Calculation of heat loss of storage tanks Global conditions Product temperature ϑ P 50 C Inside pressure p i Pa Air temperature ϑ L -20 C Wind speed u W 10 m/s Ground temperature -20 C Geometry of storage tank Ground plan Round sketch Tank inside diameter D T mm Circumference mm Area m² ϑ B Tank height Filling level H T H F mm mm Properties Storage medium HFO 180 Density ρ kg/m³ Specific heat capacity cp 1930 J/(kg K) Thermal conductivity λ W/(m K) Dynamic viscosity η 171 mpa s Kinematic viscosity ν 1.904e-4 m²/s Coefficient of thermal expansion β 7.072e-4 1/K Gas above storage medium Medium name Air Density ρ kg/m³ Specific heat capacity cp 1008 J/(kg K) Thermal conductivity λ W/(m K) Dynamic viscosity η mpa s Kinematic viscosity ν 1.803e-5 m²/s Coefficient of thermal expansion β /K Wall thickness and thermal conductivity of baseplate, tank and the insulation Bottom Shell Roof Thickness of the 8 mm 8 mm 8 mm wall Thermal conductivity 52 W/(m K) 52 W/(m K) 52 W/(m K) Insulation thickness mm 100 mm 100 mm Thermal conductivity Soil Thermal conductivity Heat losses W/(m K) 0.04 W/(m K) 0.04 W/(m K) 2 W/(m K) Bottom Shell Roof 3.28 kw wet part kw kw dry part kw Total heat loss Q total kw Lauterbach Verfahrenstechnik GmbH
4 Bottom Thickness of the wall Thermal conductivity of the wall Thermal resistance of the wall Thickness of the insulation Thermal conductivity of the insulation Thermal resistance of the insulation Heat transfer coefficient inside Thermal conductivity of soil s W,B λ W,B β W,B s Insu,B λ Insu,B β Insu,B α i,b λ Soil 8 mm 52 W/(m K) 1.538e-4 m² K/W mm W/(m K) m² K/W 17.5 W/(m² K) 2 W/(m K) Contact surface A B m² Correction factor for contact surface c A,B 1 Wall temperature inside, bottom ϑ i,b C Temperature (wall-insulation) ϑ g,b C Temperature outside, bottom Heat flow to outside ϑ a,b C 3.28 kw Q a,b Shell Thickness of the wall Thermal conductivity of the wall Thermal resistance of the wall Thickness of the insulation Thermal conductivity of the insulation Thermal resistance of the insulation Heat transfer coefficient outside s W,M λ W,M β W,M s Insu,M λ Insu,M β Insu,M α a,m 8 mm 52 W/(m K) 1.538e-4 m² K/W 100 mm 0.04 W/(m K) 2.5 m² K/W W/(m² K) Shell wet part Heat transfer coefficient inside α i,m,b W/(m² K) Contact surface A M,b m² Correction factor for contact surface c A,M,b 1 Wall temperature inside, shell ϑ i,m,b C Temperature (wall-insulation) Temperature insulation outside, shell ϑ g,m,b C C ϑ a,m,b Heating performance Heat flow from inside Heat flow to outside Q h,m,b Q i,m,b Q a,m,b 0 kw kw kw Shell dry part Heat transfer coefficient inside α i,m,t W/(m² K) Contact surface A M,t 37.7 m² Correction factor for contact surface c A,M,t 1 Wall temperature inside, shell ϑ i,m,t C Temperature (wall-insulation) Temperature insulation outside, shell ϑ g,m,t C C ϑ a,m,t Heating performance Heat flow from inside Heat flow to outside Q h,m,t Q i,m,t Q a,m,t 0 kw kw kw Lauterbach Verfahrenstechnik GmbH
5 Roof Thickness of the wall Thermal conductivity of the wall Thermal resistance of the wall Thickness of the insulation Thermal conductivity of the insulation Thermal resistance of the insulation Emissivity of the roof Emissivity of the product Heat transfer coefficient outside Heat transfer coefficient inside (total) s W,D λ W,D β W,D s Insu,D λ Insu,D β Insu,D ε D ε P α a,d α i,d 8 mm 52 W/(m K) 1.538e-4 m² K/W 100 mm 0.04 W/(m K) 2.5 m² K/W W/(m² K) W/(m² K) Contact surface A D m² Correction factor for contact surface c A,D 1 Wall temperature inside, roof ϑ i,d 46.3 C Temperature (wall-insulation) Temperature insulation outside, roof ϑ g,d C C ϑ a,d Heating performance Heat flow from inside Heat flow to outside Q h,d Q i,d Q a,d 0 kw kw kw Balance Heating performance Heat flow from inside Heat flow to outside Q h,total Q i,total Q a,total kw kw kw Lauterbach Verfahrenstechnik GmbH
6 Calculation of the heating coil Number of parallel heating circuits 1 Heating medium Transcal LT Mass flow m 7957 kg/h Volume flow V 10 m³/h Pressure (abs.) P Pa Inlet temperature ϑe 140 C Outlet temperature ϑa C Mean temperature ϑm C Tube outside diameter da 60.3 mm Tube wall thickness s 2.9 mm Tube inside diameter di 54.5 mm Thermal conductivity of tube material λ R 52 W/(m K) Fouling inside Fouling outside f i 0 m² K/W 0 m² K/W Properties of the heating medium Density ρ kg/m³ Specific heat capacity cp 2349 J/(kg K) Thermal conductivity λ W/(m K) Dynamic viscosity η mpa s Kinematic viscosity ν 1.446e-6 m²/s Properties of the storage medium at ϑ C Density ρ kg/m³ Specific heat capacity cp 2064 J/(kg K) Thermal conductivity λ W/(m K) Dynamic viscosity η mpa s Kinematic viscosity ν 3.68e-5 m²/s Coefficient of thermal expansion β 7.209e-4 1/K Result Tube-side velocity u m/s Heat transfer coefficient inside α i 1101 W/(m² K) Heat transfer coefficient outside α a 127 W/(m² K) Overall heat transfer coefficient k W/(m² K) Pressure drop (straight tube without bends) P 2819 Pa Tube length per heating circuit L mm Area per heating circuits A m² Total tube length of all heating circuits Total area of all heating circuits L total mm m² f a A total Lauterbach Verfahrenstechnik GmbH
7 Properties ambient air Properties of air State 1 State 2 Temperature ϑ C ϑ 2 C Pressure p bar p 2 bar Density ρ kg/m³ ρ kg/m³ Specific heat capacity c p 1006 J/(kg K) c p J/(kg K) Thermal conductivity λ W/(m K) λ W/(m K) Dynamic viscosity η mpa s η mpa s Kinematic viscosity ν 1.166e-5 m²/s ν m²/s Prandtl number Pr Pr Thermal diffusivity a 1.632e-5 m²/s a m²/s Compressibility factor Z Z Specific enthalpy h J/kg h J/kg Specific entropy s J/(kg K) s J/(kg K) Coefficient of thermal expansion β /K β 1/K Speed of sound w m/s w m/s Constants Molecular weight M g/mol Gas constant R J/(kg K) Standard density kg/m³ Critical data Critical temperature T c C Critical pressure p c Pa Critical density kg/m³ Validity range -150 C ϑ 1000 C 1 bar p 1000 bar Composition of the air Mol-% Wt-% N 2 : O 2 : Ar: Normalization of Enthalpy and Entropy h = 0 kj/kg, s = 0 kj/(kg K) T = K = 25 C, p = bar for the pure components ρ N ρ c Lauterbach Verfahrenstechnik GmbH
8 Heat transfer outside, roof Heat transfer in flow past a plane wall Geometry Heated plate length l mm Flow velocity w 10 m/s Properties Mean pressure p Pa Mean temperature ϑ -20 C Fluid liquid /gaseous? Density Specific heat capacity Thermal conductivity Dynamic viscosity Kinematic viscosity Prandtl number ρ cp λ η ν Pr gaseous kg/m³ 1006 J/(kg K) W/(m K) mpa s 1.166e-5 m²/s Mean wall temperature C Exponent for gases 0.12 Heat transfer Reynolds number Re 1.03e+7 Nusselt number laminar Nu lam 1904 (1) Nusselt number turbulent Nu turb (2) Nusselt number average Nu l, (5) Nusselt number with wall correction Nu (6) Heat transfer coefficient α W/(m² K) Equations ϑ W n G (1) (2) (5) (6) Correction factor K (Effect of temperature dependent property variations) Gases Lauterbach Verfahrenstechnik GmbH
9 Properties tank medium Properties of heavy fuel oils Properties of Heavy Fuel Oils (HFO) Selected oil: HFO 180 Oil selection: 7 State 1 State 2 Temperature ϑ 50 C ϑ C Density ρ kg/m³ ρ kg/m³ Specific heat capacity cp 1930 J/(kg K) cp 2065 J/(kg K) Thermal conductivity λ W/(m K) λ W/(m K) Dynamic viscosity η 171 mpa s η mpa s Kinematic viscosity ν 1.904e-4 m²/s ν 3.681e-5 m²/s Prandtl number Pr 2661 Pr Coefficient of thermal expansion β 7.072e-4 1/K β 7.211e-4 1/K Thermal diffusivity a 7.155e-8 m²/s a 6.722e-8 m²/s Pr = ν/a = η cp/λ a = λ/(ρ cp) Lauterbach Verfahrenstechnik GmbH
10 Inside heat transfer coefficient, bottom Heat transfer by natural convection around immersed bodies 4. Horizontal plane surfaces Heat emission at upper side (lower surface cooled) Boundary conditions Area of the body flown-around A m² Perimeter of the projection surface U mm Characteristic length l 3000 mm (11) Acceleration due to gravity g 9.81 m/s² Temperature on the surface ϑ C Temperature of fluid outside the boundary layer ϑ 50 C Temperature difference (ϑ 0 - ϑ ) ϑ K Properties Mean temperature (ϑ 0 + ϑ ) / 2 ϑ m C Density ρ kg/m³ Specific heat capacity c p 1930 J/(kg K) Dynamic viscosity η 171 mpa s Kinematic viscosity ν 1.904e-4 m²/s Thermal conductivity λ W/(m K) Coefficient of thermal expansion β 7.072e-4 1/K Characteristic values Prandtl number Pr = ν ρ c p / λ Pr 2661 Grashof number Gr = g l 3 β ϑ / ν 2 Gr (3) Rayleigh number Ra = Gr Pr Ra 2.28e+10 (4) Prandtl function f 2 (Pr) (20) Nusselt number laminar Nu l (18) Nusselt number turbulent Nu t (19) Nusselt number Nu Heat transfer Heat transfer coefficient α = Nu λ / l α a 17.5 W/(m² K) (2) Exchange surface A m² Convective heat flux Q kw Equations (2) (3) (4) (11) (18) (19) (20) Lauterbach Verfahrenstechnik GmbH
11 Lauterbach Verfahrenstechnik GmbH
12 Gas properties Properties of air State 1 State 2 Temperature ϑ C ϑ 2 C Pressure p 1 1 bar p 2 bar Density ρ kg/m³ ρ kg/m³ Specific heat capacity c p 1008 J/(kg K) c p J/(kg K) Thermal conductivity λ W/(m K) λ W/(m K) Dynamic viscosity η mpa s η mpa s Kinematic viscosity ν 1.803e-5 m²/s ν m²/s Prandtl number Pr Pr Thermal diffusivity a 2.559e-5 m²/s a m²/s Compressibility factor Z Z Specific enthalpy h J/kg h J/kg Specific entropy s J/(kg K) s J/(kg K) Coefficient of thermal expansion β /K β 1/K Speed of sound w m/s w m/s Constants Molecular weight M g/mol Gas constant R J/(kg K) Standard density kg/m³ Critical data Critical temperature T c C Critical pressure p c Pa Critical density kg/m³ Validity range -150 C ϑ 1000 C 1 bar p 1000 bar Composition of the air Mol-% Wt-% N 2 : O 2 : Ar: Normalization of Enthalpy and Entropy h = 0 kj/kg, s = 0 kj/(kg K) T = K = 25 C, p = bar for the pure components ρ N ρ c Lauterbach Verfahrenstechnik GmbH
13 Heat transfer outside, shell Heat loss of walls and pipeworks Heat loss in insulated pipelines (exposed) Parameters Temperature medium inside ϑ i 50 C Air temperature ϑ a -20 C Inside diameter of the pipe d mm Inside heat transfer coefficient α i W/(m² K) Wind velocity w 10 m/s Heat transfer Thickness Thermal conductivity Tube wall s 0 8 mm λ 0 52 W/(m K) Insulation 1 s mm λ W/(m K) Insulation 2 s 2 0 mm λ 2 1 W/(m K) Calculation Outside diameter of the pipe d mm Outside diameter of the insulation 1 d mm Outside diameter of the insulation 2 d mm Temperature difference ϑ i -ϑ a 70 C Auxiliary variable D m² K/W Outside heat transfer coefficient α a W/(m² K) Heat loss per unit of length Q/l W/m Pipe length l mm Heat loss absolute Q kw Temperatures Temperature medium inside ϑ i 50 C Wall temperature inside ϑ Wi C Wall temperature outside ϑ Wa C Insulation ϑ Iso C Surface temperature ϑ o C Air temperature -20 C Equations ϑ a For wind (w>0) follows Lauterbach Verfahrenstechnik GmbH
14 Inside heat transfer coefficient, wet shell Heat transfer by natural convection around immersed bodies 2. Vertical areas (Cylinder) Boundary conditions Height of the cylinder h mm Diameter of the cylinder D mm Characteristic length l mm Acceleration due to gravity g 9.81 m/s² Temperature on the surface ϑ C Temperature of fluid outside the boundary layer ϑ 50 C Temperature difference (ϑ 0 - ϑ ) ϑ K Properties Mean temperature (ϑ 0 + ϑ ) / 2 ϑ m C Density ρ kg/m³ Specific heat capacity c p 1930 J/(kg K) Dynamic viscosity η 171 mpa s Kinematic viscosity ν 1.904e-4 m²/s Thermal conductivity λ W/(m K) Coefficient of thermal expansion β 7.072e-4 1/K Characteristic values Prandtl number Pr = ν ρ c p / λ Pr 2661 Grashof number Gr = g l 3 β ϑ / ν 2 Gr 8.059e+8 (3) Rayleigh number Ra = Gr Pr Ra 2.14e+12 (4) Prandtl function f 1 (Pr) (13) Nusselt number for plate Nu P 1995 (12) Nusselt number Nu 1996 (14) Heat transfer Heat transfer coefficient α = Nu λ / l α W/(m² K) (2) Exchange surface A m² Convective heat flux Q kw Equations (2) (3) (4) (12) (13) (14) Lauterbach Verfahrenstechnik GmbH
15 Inside heat transfer coefficient, dry shell Heat transfer by natural convection around immersed bodies 2. Vertical areas (Cylinder) Boundary conditions Height of the cylinder h 1000 mm Diameter of the cylinder D mm Characteristic length l 1000 mm Acceleration due to gravity g 9.81 m/s² Temperature on the surface ϑ C Temperature of fluid outside the boundary layer ϑ 50 C Temperature difference (ϑ 0 - ϑ ) ϑ K Properties Mean temperature (ϑ 0 + ϑ ) / 2 ϑ m C Density ρ kg/m³ Specific heat capacity c p 1008 J/(kg K) Dynamic viscosity η mpa s Kinematic viscosity ν 1.803e-5 m²/s Thermal conductivity λ W/(m K) Coefficient of thermal expansion β /K Characteristic values Prandtl number Pr = ν ρ c p / λ Pr Grashof number Gr = g l 3 β ϑ / ν 2 Gr 7.974e+8 (3) Rayleigh number Ra = Gr Pr Ra 5.62e+8 (4) Prandtl function f 1 (Pr) (13) Nusselt number for plate Nu P (12) Nusselt number Nu (14) Heat transfer Heat transfer coefficient α = Nu λ / l α W/(m² K) (2) Exchange surface A 37.7 m² Convective heat flux Q kw Equations (2) (3) (4) (12) (13) (14) Lauterbach Verfahrenstechnik GmbH
16 Inside heat transfer coefficient, roof Heat transfer by free convection in enclosed fluid layers Horizontal flat layers (heated from below) Boundary conditions Layer thickness s 1000 mm Heated area A m² Emission rate of the heated surface (Ka) ε Emission rate of the cooled surface (Ka) 0.8 Acceleration due to gravity g 9.81 m/s² Temperature on the heated surface ϑ 1 50 C Temperature on the cooled surface ϑ C Temperature difference (ϑ 1 - ϑ 2 ) ϑ K Temperature difference (T1 4 - T2 4 ) T 4.914e+8 K^4 Properties Mean temperature ϑ m C Density ρ kg/m³ Specific heat capacity cp 1008 J/(kg K) Dynamic viscosity η mpa s Kinematic viscosity ν 1.803e-5 m²/s Thermal conductivity λ W/(m K) Thermal diffusivity a 2.559e-5 m²/s Coefficient of expansion β /K Characteristic values Grashof number Gr s 3.485e+8 (6) Prandtl number Pr (7) Rayleigh number Ra s 2.456e+8 (8) Nusselt number Nu s (11/12) Heat transfer Heat transfer coefficient α 1.51 W/(m² K) (5) Heat flux (conduction and convection) kw (3) Radiation exchange coefficient C e-8 Ka (7) Heat flux (radiation) kw Ka (6) ε 2 Q LK Q S Total heat flux Equivalent heat transfer coefficient Q SLK α SLK kw W/(m² K) Lauterbach Verfahrenstechnik GmbH
17 Equations (6) (7) (8) - without convection Ra s < 1708 Nu s = 1 - laminar 1708 Ra s < Nu s = Ra 0.25 s (11) - turbulent Ra s Nu s = Ra 0.33 s (12) (5) (3) Lauterbach Verfahrenstechnik GmbH
18 Physical properties of heating medium Properties of thermal oils Name of the oil Material structure Manufacturer Former product / Comment Range of application Transcal LT naphthene base BP State 1 State 2 Temperature C C Density ρ kg/m³ 802 kg/m³ Specific heat capacity cp 2349 J/(kg K) 2316 J/(kg K) Thermal conductivity λ W/(m K) W/(m K) Dynamic viscosity η mpa s mpa s Kinematic viscosity ν 1.355e-6 m²/s 1.573e-6 m²/s Prandtl number Pr Coef. of thermal expansion β 7.733e-4 1/K 7.794e-4 1/K Thermal diffusivity a 6.679e-8 m²/s 6.752e-8 m²/s Specific enthalpy h 0 kj/kg 0 kj/kg Vapour pressure Pa Pa Pour point -54 C Initial boiling point 290 C Minimum operating temperature -20 C Maximum operating temperature 260 C Minimum temperature filling -20 C Minimum temperature startup 71 C Maximum film temperature 280 C Flash point 155 C Ignition temperature 240 C Neutralization number 0.01 mgkoh/g Coke residue 0.01 % Explosion limit Vol-% Molecular weight kg/kmol p D Temperature ϑ max Density ρ 900 kg/m³ 732 Specific heat capacity cp 1800 J/(kg K) 2770 Thermal conductivity λ W/(m K) Dynamic viscosity η 730 mpa s 0.35 Kinematic viscosity ν 3e-4 m²/s 4.9e-7 Vapour pressure Pa p D ϑ min kg/m³ J/(kg K) W/(m K) mpa s m²/s Pa Lauterbach Verfahrenstechnik GmbH
19 Tube-side heat transfer Heat transfer in pipe flow Constant wall temperature Inlet temperature ϑ e 140 C Outlet temperature Mean temperature ϑ a C C ϑ m Physical properties Fluid liquid /gaseous? liquid Density ρ kg/m³ Specific heat capacity cp 2349 J/(kg K) Thermal conductivity λ W/(m K) Dynamic viscosity η mpa s Kinematic viscosity ν 1.446e-6 m²/s Prandtl number Pr Prandtl number at wall temperature Wall temperature Pr W C ϑ W Tube circular / non-circular? Circular tubes Tube length l mm Tube inside diameter d i 54.5 mm Cross sectional area of the tube f m² Perimeter of the tube Hydraulic diameter u mm 54.5 mm Total mass flow Total volume flow 7957 kg/h 10 m³/h Number of tubes with parallel flow Z 1 Mass flow per tube m 7957 kg/h Flow velocity w m/s d h m tot V tot Heat transfer Reynolds number Nusselt number Heat transfer coefficient Re Nu α W/(m² K) Heat duty Q = m tot c p (ϑ a - ϑ e ) Q kw Lauterbach Verfahrenstechnik GmbH
20 Results Turbulent flow (Re > 10000) Constant wall temperature Correction factor K (Effect of temperature dependent property variations) Liquids Lauterbach Verfahrenstechnik GmbH
21 Heat transfer coil around tubes Heat transfer by natural convection around immersed bodies 5. Horizontal curved areas (Cylinder) Cylinder Outside diameter d o 60.3 mm Wall thickness s 2.9 mm Inside diameter d i 54.5 mm Thermal conductivity λ 52 W/(m K) Characteristic length l mm Acceleration due to gravity g 9.81 m/s² Temperatures and properties Temperature on the surface ϑ C Temperature of fluid outside the boundary layer ϑ 50 C Temperature difference (ϑ 0 - ϑ ) ϑ K Mean temperature (ϑ 0 + ϑ ) / 2 ϑ m C Density ρ kg/m³ Specific heat capacity c p 2064 J/(kg K) Dynamic viscosity η mpa s Kinematic viscosity ν 3.68e-5 m²/s Thermal conductivity λ W/(m K) Coefficient of thermal expansion β 7.209e-4 1/K Characteristic values Prandtl number Pr = ν ρ c p / λ Pr Grashof number Gr = g l 3 β ϑ / ν 2 Gr (3) Rayleigh number Ra = Gr Pr Ra 1.881e+8 (4) Prandtl function f 3 (Pr) (24) Nusselt number Nu (22) Heat transfer Heat transfer coefficient (free α = Nu λ / l α a 127 W/(m² K) (2) convection) Convective heat flux Q kw Balance for the calculation of the surface temperature Heating medium Specific heat capacity c p 2349 J/(kg K) Density ρ kg/m³ Mass flow m 7957 kg/h Volume flow V 10 m³/h Inlet temperature ϑ e 140 C Outlet temperature Mean temperature ϑ a C C ϑ m Duty Q H kw Tube-side velocity u m/s Heat transfer coefficient inside α i 1101 W/(m² K) Fouling inside f i 0 m² K/W Fouling outside f a 0 m² K/W Overall heat transfer coefficient k W/(m² K) Length of the cylinder L mm Area of the cylinder A m² Lauterbach Verfahrenstechnik GmbH
22 Equations (2) (3) (4) (22) (24) Lauterbach Verfahrenstechnik GmbH
23 Pressure drop in coil Pressure drop in flow through pipes Straight pipes Parameters of the pipe Pipe length l m Pipe inside diameter d i 54.5 mm Absolute roughness k 0.04 mm Number of pipes with parallel flow N R 1 Physical properties Density ρ kg/m³ Dynamic viscosity η mpa s Kinematic viscosity ν 1.446e-6 m²/s Total mass flow m g 2.21 kg/s Mass flow per pipe m R 7957 kg/h Volume flow per pipe V R 10 m³/h Velocity w m/s Results Flow pattern Turbulent flow (Re > 2320) Pressure drop p 2819 Pa Reynolds number Re Drag coefficient ξ Equations Re = > 2320 Turbulent flow Lauterbach Verfahrenstechnik GmbH
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