What is the velocity of fluid flow through the 200 mm diameter pipe after being divided from a 3 m/s flow in a 450 mm diameter pipe? Option a) 2.5 m/s b) 5.55 m/s c) 7.25 m/s d) 9.56 m/s
The velocity of fluid flow through the 200 mm pipe, after a 3 m/s flow in a 450 mm pipe is divided into a 300 mm pipe flowing at 2.5 m/s and the 200mm one, is calculated to be 5.55 m/s, applying the principle of conservation of mass in fluid mechanics.
Explanation:
Fluid Mechanics and Conservation of Mass:
Fluid mechanics is a branch of physics that deals with the study of fluids in motion. In this scenario, the principle of conservation of mass is applied to analyze the flow of fluid through different pipes in a system.
Initial Conditions:
- Diameter of the main pipe: 450 mm
- Velocity in the main pipe: 3 m/s
- Diameter of the first pipe after division: 300 mm
- Velocity in the first pipe: 2.5 m/s
- Diameter of the second pipe after division: 200 mm
- Unknown: Velocity in the second pipe
Calculation Process:
1. Calculate the mass flow rate in the main pipe:
Mass flow rate = Cross-sectional area x Velocity
Mass flow rate in the main pipe = (π * 0.45² / 4) * 3
2. Calculate the mass flow rate in the first pipe:
Mass flow rate in the first pipe = (π * 0.3² / 4) * 2.5
3. Determine the mass flow rate in the second pipe:
Mass flow rate in the second pipe = Mass flow rate in main pipe - Mass flow rate in first pipe
4. Calculate the velocity in the second pipe:
Velocity in the second pipe = Mass flow rate in the second pipe / (π * 0.2² / 4)
Final Result:
By following the conservation of mass principle and performing the calculations, the velocity of fluid flow through the 200 mm diameter pipe is determined to be 5.55 m/s.
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