Is length directly proportional to cross-sectional area and velocity increase and the pressure decrease when water flowing in a broader pipe enters a narrow pipe?
Prompt: Is length directly proportional to cross-sectional area & velocity increase & pressure decrease when water flowing in broader pipe enters narrow pipe?
Response:
No, the statements about the relationships between length, cross-sectional area, velocity, and pressure are not entirely accurate. Here's a breakdown:
Therefore, while the velocity increases in the narrower section due to continuity, the pressure drop depends on the frictional losses throughout the entire pipe system.
Additional considerations:
- The rate of pressure decrease due to friction depends on several factors, including:Pipe material (roughness) Flow rate Pipe diameter Fluid viscosity
- In some cases, if the narrowing is sudden and significant, localized pressure increases can occur due to energy conversion from kinetic energy (velocity) to pressure.
The length and cross-sectional area of a conductor directly influence its electrical resistance. Length is directly proportional to resistance, while cross-sectional area is inversely proportional. Speed increases when cross-sectional area decreases, and speed decreases when cross-sectional area increases. This is a consequence of the continuity equation. If the flow Q is held constant, when the area A decreases, the velocity v must increase proportionally. The area of the cross-section is inversely proportional to resistance because: Resistance inside a conductor is caused by the collision of charged particles or electrons with each other. When the area of the cross-section of the conductor is increased space between charged particles will also increase. Resistance is proportional to resistivity and length, and inversely proportional to cross sectional area. As the cross-sectional area increases, velocity decreases. Arteries and veins have smaller cross-sectional areas and the highest velocities, whereas capillaries have the most cross-sectional area and the lowest velocities. The velocity v of a fluid flowing in a conduit is inversely proportional to the cross-sectional area of the conduit. The fluid velocity increases, the pressure of the fluid decreases. Therefore, the pressure of the fluid decreases as the pipe becomes narrower. Principle of continuity av = a constant or v ∝ 1/a i.e. as the water flows from wider tube to narrow tube its velocity increases. According to Bernoullis Principle P + 1/2 ρv2 = a constant where velocity is large the pressure is less. In a stream-line flow of a liquid according to equation of continuity av = a constant where a is the area of cross-section and v is the velocity of the liquid flow. When water flowing in broader pipe enters a narrow pipe the area of cross-section of the water decreases therefore the velocity of water increases. The higher pressure in the wide part pushes on the fluid in the narrow part and accelerates that fluid. So the fluid in the narrow part starts moving faster. Now the fluid in the narrow part not only has lower pressure but also a higher speed—because it was accelerated by the higher-pressure fluid behind it. As the velocity of the flow increases, the organization increases, and the pressure drops further. The organization and density increase is a result of the fluid doing work on itself.
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