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Venturi flow rate

Input interpretation

Venturi flow rate
Venturi flow rate

Equation

Q = π (D_1^2 sqrt((2 (P_1 - P_2))/ρ))/(4 sqrt(D_1^4/D_2^4 - 1)) | Q | flow rate ρ | fluid density P_1 | upstream pressure P_2 | downstream pressure D_1 | upstream pipe diameter D_2 | downstream pipe diameter (Q is the flow rate as measured by a Venturi flow meter)
Q = π (D_1^2 sqrt((2 (P_1 - P_2))/ρ))/(4 sqrt(D_1^4/D_2^4 - 1)) | Q | flow rate ρ | fluid density P_1 | upstream pressure P_2 | downstream pressure D_1 | upstream pipe diameter D_2 | downstream pipe diameter (Q is the flow rate as measured by a Venturi flow meter)
Equation
Equation

Input values

fluid density | 1000 kg/m^3 (kilograms per cubic meter) upstream pressure | 40 Pa (pascals) downstream pressure | 20 Pa (pascals) upstream pipe diameter | 0.02 meters downstream pipe diameter | 0.01 meters
fluid density | 1000 kg/m^3 (kilograms per cubic meter) upstream pressure | 40 Pa (pascals) downstream pressure | 20 Pa (pascals) upstream pipe diameter | 0.02 meters downstream pipe diameter | 0.01 meters

Results

flow rate | 16.22 mL/s (milliliters per second) = 15.43 gal/h (gallons per hour) = 0.01622 L/s (liters per second) = 973.4 mL/min (milliliters per minute) = 0.9734 L/min (liters per minute) = 58403 mL/h (milliliters per hour) = 1402 L/day (liters per day) = 973.4 cm^3/min (cubic centimeters per minute)
flow rate | 16.22 mL/s (milliliters per second) = 15.43 gal/h (gallons per hour) = 0.01622 L/s (liters per second) = 973.4 mL/min (milliliters per minute) = 0.9734 L/min (liters per minute) = 58403 mL/h (milliliters per hour) = 1402 L/day (liters per day) = 973.4 cm^3/min (cubic centimeters per minute)

Possible intermediate steps

Calculate the flow rate using the following information: known variables | | ρ | fluid density | 1000 kg/m^3 P_1 | upstream pressure | 40 Pa P_2 | downstream pressure | 20 Pa D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m Convert known variables into appropriate units using the following: 1 kg/m^3 = 1000 g/m^3: 1 Pa = 1000 g/(m s^2): 1 Pa = 1000 g/(m s^2): known variables | | ρ | fluid density | 1×10^6 g/m^3 P_1 | upstream pressure | 40000 g/(m s^2) P_2 | downstream pressure | 20000 g/(m s^2) D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m The relevant equation that relates flow rate (Q), fluid density (ρ), upstream pressure (P_1), downstream pressure (P_2), upstream pipe diameter (D_1), and downstream pipe diameter (D_2) is: Q = (π (D_1^2 sqrt((2 (P_1 - P_2))/ρ)))/(4 sqrt(D_1^4/D_2^4 - 1)) Substitute known variables and constants into the equation: known variables | | ρ | fluid density | 1×10^6 g/m^3 P_1 | upstream pressure | 40000 g/(m s^2) P_2 | downstream pressure | 20000 g/(m s^2) D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m constant | | π | pi | 3.14159 | : Q = (3.14159 ((0.02 m)^2 sqrt((2 (40000 g/(m s^2) - 20000 g/(m s^2)))/(1×10^6 g/m^3))))/(4 sqrt((0.02 m)^4/(0.01 m)^4 - 1)) Separate the numerical part, (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)), from the unit part, (m^2 sqrt((g/(m s^2) + g/(m s^2))/(g/m^3)))/sqrt((m^4)/(m^4)) = m^3/s: Q = (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)) m^3/s Evaluate (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)): Q = 1.6223×10^-5 m^3/s Convert 1.6223×10^-5 m^3/s into mL/s (milliliters per second) using the following: 1 m^3/s = 1×10^6 mL/s: Answer: | | Q = 16.22 mL/s
Calculate the flow rate using the following information: known variables | | ρ | fluid density | 1000 kg/m^3 P_1 | upstream pressure | 40 Pa P_2 | downstream pressure | 20 Pa D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m Convert known variables into appropriate units using the following: 1 kg/m^3 = 1000 g/m^3: 1 Pa = 1000 g/(m s^2): 1 Pa = 1000 g/(m s^2): known variables | | ρ | fluid density | 1×10^6 g/m^3 P_1 | upstream pressure | 40000 g/(m s^2) P_2 | downstream pressure | 20000 g/(m s^2) D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m The relevant equation that relates flow rate (Q), fluid density (ρ), upstream pressure (P_1), downstream pressure (P_2), upstream pipe diameter (D_1), and downstream pipe diameter (D_2) is: Q = (π (D_1^2 sqrt((2 (P_1 - P_2))/ρ)))/(4 sqrt(D_1^4/D_2^4 - 1)) Substitute known variables and constants into the equation: known variables | | ρ | fluid density | 1×10^6 g/m^3 P_1 | upstream pressure | 40000 g/(m s^2) P_2 | downstream pressure | 20000 g/(m s^2) D_1 | upstream pipe diameter | 0.02 m D_2 | downstream pipe diameter | 0.01 m constant | | π | pi | 3.14159 | : Q = (3.14159 ((0.02 m)^2 sqrt((2 (40000 g/(m s^2) - 20000 g/(m s^2)))/(1×10^6 g/m^3))))/(4 sqrt((0.02 m)^4/(0.01 m)^4 - 1)) Separate the numerical part, (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)), from the unit part, (m^2 sqrt((g/(m s^2) + g/(m s^2))/(g/m^3)))/sqrt((m^4)/(m^4)) = m^3/s: Q = (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)) m^3/s Evaluate (3.14159 ((0.02)^2 sqrt((2 (40000 - 20000))/(1×10^6))))/(4 sqrt((0.02)^4/(0.01)^4 - 1)): Q = 1.6223×10^-5 m^3/s Convert 1.6223×10^-5 m^3/s into mL/s (milliliters per second) using the following: 1 m^3/s = 1×10^6 mL/s: Answer: | | Q = 16.22 mL/s

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