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In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.?
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In a pipeline with a diameter of 500mm, a venturi meter is installed. ...
Given:
Pipeline diameter (D) = 500 mm
Throat pipe diameter (d) = 0.5D = 0.5 * 500 mm = 250 mm
Pressure in pipeline (P1) = 1.5 kg/cm^2
Pressure at throat (P2) = 40 cm Hg (Vacuum)
Loss in differential head = 4%
Calculations:
1. Coefficient of Discharge (Cd):
The coefficient of discharge (Cd) is a dimensionless factor that relates the actual flow rate through the venturi meter to the theoretical flow rate. It takes into account the losses in the meter and the contraction and expansion of the flow.
The pressure difference (ΔP) across the venturi meter can be calculated using the pressure at the throat (P2) and the pressure in the pipeline (P1):
ΔP = P1 - P2
The theoretical flow rate (Qth) can be calculated using the pressure difference (ΔP) and the diameter of the throat (d):
Qth = Cd * A * sqrt(2 * ΔP / ρ)
Where A is the cross-sectional area of the throat and ρ is the density of the fluid.
To find the coefficient of discharge (Cd), we need to find the actual flow rate (Qa). The actual flow rate can be calculated using the loss in differential head (L):
Qa = (100 - L) / 100 * Qth
Substituting the values and rearranging the equation, we can solve for Cd:
Cd = Qa / (A * sqrt(2 * ΔP / ρ))
2. Flow Rate (Q):
The flow rate (Q) can be calculated using the actual flow rate (Qa) and the cross-sectional area of the pipeline (A):
Q = Qa * (Athroat / Apipeline)
Where Athroat is the cross-sectional area of the throat and Apipeline is the cross-sectional area of the pipeline.
Conversion of Units:
Before performing calculations, we need to convert the given units to a consistent system. In this case, we will convert all units to SI units (meters, kilograms, and seconds).
- Convert pipeline diameter (D) from mm to meters: D = 500 mm = 0.5 meters
- Convert throat pipe diameter (d) from mm to meters: d = 250 mm = 0.25 meters
- Convert pressure in pipeline (P1) from kg/cm^2 to Pa: P1 = 1.5 kg/cm^2 = 1.5 * 10^4 Pa
- Convert pressure at throat (P2) from cm Hg to Pa: P2 = 40 cm Hg * 133.322 Pa/cm Hg = 5332.88 Pa
- Assume the density of the fluid (ρ) is 1000 kg/m^3 (for water)
Calculating Coefficient of Discharge (Cd):
- Calculate the pressure difference (ΔP):
ΔP = P1 - P2 = 1.5 * 10^4 Pa - 5332.88 Pa = 9.46672 * 10^3 Pa
- Calculate the theoretical flow rate (Qth
Pipeline diameter (D) = 500 mm
Throat pipe diameter (d) = 0.5D = 0.5 * 500 mm = 250 mm
Pressure in pipeline (P1) = 1.5 kg/cm^2
Pressure at throat (P2) = 40 cm Hg (Vacuum)
Loss in differential head = 4%
Calculations:
1. Coefficient of Discharge (Cd):
The coefficient of discharge (Cd) is a dimensionless factor that relates the actual flow rate through the venturi meter to the theoretical flow rate. It takes into account the losses in the meter and the contraction and expansion of the flow.
The pressure difference (ΔP) across the venturi meter can be calculated using the pressure at the throat (P2) and the pressure in the pipeline (P1):
ΔP = P1 - P2
The theoretical flow rate (Qth) can be calculated using the pressure difference (ΔP) and the diameter of the throat (d):
Qth = Cd * A * sqrt(2 * ΔP / ρ)
Where A is the cross-sectional area of the throat and ρ is the density of the fluid.
To find the coefficient of discharge (Cd), we need to find the actual flow rate (Qa). The actual flow rate can be calculated using the loss in differential head (L):
Qa = (100 - L) / 100 * Qth
Substituting the values and rearranging the equation, we can solve for Cd:
Cd = Qa / (A * sqrt(2 * ΔP / ρ))
2. Flow Rate (Q):
The flow rate (Q) can be calculated using the actual flow rate (Qa) and the cross-sectional area of the pipeline (A):
Q = Qa * (Athroat / Apipeline)
Where Athroat is the cross-sectional area of the throat and Apipeline is the cross-sectional area of the pipeline.
Conversion of Units:
Before performing calculations, we need to convert the given units to a consistent system. In this case, we will convert all units to SI units (meters, kilograms, and seconds).
- Convert pipeline diameter (D) from mm to meters: D = 500 mm = 0.5 meters
- Convert throat pipe diameter (d) from mm to meters: d = 250 mm = 0.25 meters
- Convert pressure in pipeline (P1) from kg/cm^2 to Pa: P1 = 1.5 kg/cm^2 = 1.5 * 10^4 Pa
- Convert pressure at throat (P2) from cm Hg to Pa: P2 = 40 cm Hg * 133.322 Pa/cm Hg = 5332.88 Pa
- Assume the density of the fluid (ρ) is 1000 kg/m^3 (for water)
Calculating Coefficient of Discharge (Cd):
- Calculate the pressure difference (ΔP):
ΔP = P1 - P2 = 1.5 * 10^4 Pa - 5332.88 Pa = 9.46672 * 10^3 Pa
- Calculate the theoretical flow rate (Qth
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In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.?
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In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.?.
In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a pipeline with a diameter of 500mm, a venturi meter is installed. The ratio of the throat pipe diameter to the pipeline diameter is 0.5. The pressure in the pipeline is 1.5 kg/cm^2, and at the throat, it is 40 cm Hg (Vacuum). If there is a 4% loss in the differential head between the gauges, a. Determine the coefficient of discharge…………? b. calculate the flow rate in the pipeline in cubic meters per second.?.
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