Velocity of a fluid within a pipe

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Homework Help Overview

The discussion revolves around modeling the flow of blood through a hollow pipe, specifically examining the effects of a constriction in the pipe's diameter on fluid velocity. The problem involves fluid dynamics principles, particularly focusing on the application of Bernoulli's equation and mass flow conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Bernoulli's equation and the conservation of mass in fluid flow. There is an attempt to clarify the relationship between pressures and fluid velocities at different points in the pipe. Questions arise regarding the definitions of pressure and density in the context of the problem.

Discussion Status

Some participants have offered guidance on using mass flow conservation instead of focusing on pressure values. There is an ongoing exploration of the relevant equations and concepts, with no explicit consensus reached yet.

Contextual Notes

Participants note that the fluid (blood) is assumed to be incompressible, which influences the approach to solving the problem. There is also a mention of the specific diameters of the pipe sections involved in the discussion.

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Homework Statement



A scientist attempts to model the flow of blood through an artery using a hollow pipe of diameter 1.8cm. A fluid density 1060kg/m^3 is used to simulate blood in the pipe. Viscous effects can be considered to be negligible.

TO study a blockage in an artery, the scientist holds the pipe horizontally and places a constriction in the pipe reducing the diameter to 1.1 cm. What is the speed of the fluid as it passes through the narrowest point of the blockage? Assume that the speed in the un-constricted region is 0.75m/s.

Homework Equations


Bernoulli's
P1 + 1/2pV1^2 +pgh = P2 + 1/2pV2^2 +pgh


The Attempt at a Solution



I tried using Bernoullis but i keep getting stuck cause i don't know what the pressures at P1 and P2 are.
 
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You don't need any pressures, just consider that mass does not vanish in the pipe: mass flow has to be the same everywhere, and you can assume that blood cannot be compressed.
 
Ohhh, so I should use the formula p1*v1*A1 = p2*v2*A2?Thanks bud!
 
What are p1 and p2?
 
My apologies, p1 and p2 are the density. I think they're called rho?
 
Ah, okay.
Well, blood cannot be compressed (in relevant amounts).
 

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