A pipe of diameter 20 cm and length 10000 m is laid at a slope of 1 in...
Head loss due to friction in a pipeline
Given data:
- Diameter of the pipe (D) = 20 cm = 0.2 m
- Length of the pipe (L) = 10000 m
- Slope of the pipe (S) = 1 in 200
- Oil specific gravity (sp. gr.) = 0.9
- Oil viscosity (μ) = 1.5 poise
- Oil flow rate (Q) = 20 litres/sec = 0.02 m3/sec
Formula to calculate head loss due to friction in a pipeline:
hf = f x (L/D) x (V^2/2g)
where:
- hf = head loss due to friction (m)
- f = friction factor (dimensionless)
- V = average velocity of fluid (m/s)
- g = acceleration due to gravity (9.81 m/s^2)
To calculate friction factor (f), we need to use the Colebrook-White equation:
1/sqrt(f) = -2.0 x log10((ε/D)/3.7 + 2.51/(Re x sqrt(f)))
where:
- ε = pipe roughness (m)
- Re = Reynolds number (dimensionless)
- Re = (ρ x V x D) / μ
- ρ = fluid density (kg/m^3)
Assuming the pipe roughness to be 0.05 mm, we can calculate the Reynolds number as:
ρ = sp. gr. x 1000 = 900 kg/m^3
Re = (900 x 0.02 x 0.2) / 1.5 x 10^-3 = 24000
Using the Colebrook-White equation, we can iteratively solve for f, which turns out to be 0.022.
Now, we can calculate the head loss due to friction using the formula:
hf = f x (L/D) x (V^2/2g) = 0.022 x (10000/0.2) x (0.02^2/2 x 9.81) = 223.7 m
Therefore, the head loss due to friction in the pipeline is 223.7 m.
Purpose of orifice meter
An orifice meter is a type of flow meter used to measure the rate of fluid flow through a pipeline. It consists of a thin plate with a small hole (or orifice) in the center, which is inserted into the pipeline. As fluid flows through the orifice, the pressure difference across the plate is measured, which is proportional to the flow rate.
The purpose of using an orifice meter is to:
- Measure the flow rate of fluid in a pipeline accurately and reliably.
- Monitor the performance of pumps, valves, and other equipment in the pipeline.
- Detect leaks, blockages, or other problems in the pipeline.
- Determine the amount of fluid being transferred in various industrial processes, such as oil and gas production, chemical processing, and water treatment.
- Ensure compliance with regulatory requirements for flow measurement and reporting.
Magnitude and direction of resultant force on a turning pipe
Given data:
- Diameter of the pipe (D) = 0.3 m
- Head (H) = 25 m
- Velocity of water (V) = 3.5 m/s
- Angle of turn (θ) =