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Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses?
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Pipe 200 metre long slopes drawn at one in hundred and tables from 600...
Solution:
Given data:
- Length of pipe = 200 m
- Slope of pipe = 1 in 100
- Diameter of higher end = 600 mm
- Diameter of lower end = 300 mm
- Discharge = 100 L/s
- Pressure at higher end = 60 kN/m^2
Conversion:
- Length of pipe = 200 m = 0.2 km
- Discharge = 100 L/s = 0.1 m^3/s
### Velocity at the higher end:
Velocity of flow (V1) can be calculated using the discharge formula Q = A1V1, where A1 is the area of cross-section at the higher end.
- Diameter of higher end (D1) = 600 mm = 0.6 m
- Radius of higher end (r1) = 0.6/2 = 0.3 m
- Area of cross-section at higher end (A1) = πr1^2 = 0.2827 m^2
Substituting the values in the formula, we get:
0.1 = 0.2827 x V1
V1 = 0.353 m/s
### Velocity at the lower end:
Velocity of flow (V2) can be calculated using the continuity equation A1V1 = A2V2, where A2 is the area of cross-section at the lower end.
- Diameter of lower end (D2) = 300 mm = 0.3 m
- Radius of lower end (r2) = 0.3/2 = 0.15 m
- Area of cross-section at lower end (A2) = πr2^2 = 0.0707 m^2
Substituting the values in the equation, we get:
0.2827 x 0.353 = 0.0707 x V2
V2 = 1.422 m/s
### Head loss due to friction:
Using the Darcy-Weisbach equation, the head loss due to friction can be calculated as:
hL = f x (L/D) x (V^2/2g), where f is the Darcy friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of flow, and g is the acceleration due to gravity.
- Length of pipe (L) = 200 m
- Diameter of pipe at higher end (D1) = 0.6 m
- Diameter of pipe at lower end (D2) = 0.3 m
- Velocity of flow (V) = 1.422 m/s
- Acceleration due to gravity (g) = 9.81 m/s^2
The value of f can be calculated using the Colebrook equation as:
1/sqrt(f) = -2 x log10[(e/D)/3.7 + 2.51/(Re x sqrt(f))]
where e is the roughness height and Re is the Reynolds number.
Assuming the roughness height to be 0.03 mm for commercial steel pipes, the Reynolds number can be calculated as:
Re = (D1 + D2)/2 x V x ρ/μ
where ρ is the density of water and μ is the dynamic viscosity of water.
- Density of water
Given data:
- Length of pipe = 200 m
- Slope of pipe = 1 in 100
- Diameter of higher end = 600 mm
- Diameter of lower end = 300 mm
- Discharge = 100 L/s
- Pressure at higher end = 60 kN/m^2
Conversion:
- Length of pipe = 200 m = 0.2 km
- Discharge = 100 L/s = 0.1 m^3/s
### Velocity at the higher end:
Velocity of flow (V1) can be calculated using the discharge formula Q = A1V1, where A1 is the area of cross-section at the higher end.
- Diameter of higher end (D1) = 600 mm = 0.6 m
- Radius of higher end (r1) = 0.6/2 = 0.3 m
- Area of cross-section at higher end (A1) = πr1^2 = 0.2827 m^2
Substituting the values in the formula, we get:
0.1 = 0.2827 x V1
V1 = 0.353 m/s
### Velocity at the lower end:
Velocity of flow (V2) can be calculated using the continuity equation A1V1 = A2V2, where A2 is the area of cross-section at the lower end.
- Diameter of lower end (D2) = 300 mm = 0.3 m
- Radius of lower end (r2) = 0.3/2 = 0.15 m
- Area of cross-section at lower end (A2) = πr2^2 = 0.0707 m^2
Substituting the values in the equation, we get:
0.2827 x 0.353 = 0.0707 x V2
V2 = 1.422 m/s
### Head loss due to friction:
Using the Darcy-Weisbach equation, the head loss due to friction can be calculated as:
hL = f x (L/D) x (V^2/2g), where f is the Darcy friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of flow, and g is the acceleration due to gravity.
- Length of pipe (L) = 200 m
- Diameter of pipe at higher end (D1) = 0.6 m
- Diameter of pipe at lower end (D2) = 0.3 m
- Velocity of flow (V) = 1.422 m/s
- Acceleration due to gravity (g) = 9.81 m/s^2
The value of f can be calculated using the Colebrook equation as:
1/sqrt(f) = -2 x log10[(e/D)/3.7 + 2.51/(Re x sqrt(f))]
where e is the roughness height and Re is the Reynolds number.
Assuming the roughness height to be 0.03 mm for commercial steel pipes, the Reynolds number can be calculated as:
Re = (D1 + D2)/2 x V x ρ/μ
where ρ is the density of water and μ is the dynamic viscosity of water.
- Density of water
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Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses?
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Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses?.
Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe 200 metre long slopes drawn at one in hundred and tables from 600 mm diameter at the higher into 300 mm diameter at the lower end and carries hundred litres per second if the pressure gauge at the higher end read 60 kilo Newton per metre square calculate valid sheet is at the two ends and pressure at the lowest and neglecting all the losses?.
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