Velocity of a fluid within a pipe

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SUMMARY

The discussion focuses on modeling the flow of blood through an artery using a hollow pipe with a diameter of 1.8 cm, simulating blood with a density of 1060 kg/m³. A blockage is introduced by constricting the pipe to a diameter of 1.1 cm, and the initial fluid speed is 0.75 m/s. Participants clarify that to find the speed at the blockage, the mass flow rate must remain constant, leading to the application of the equation A1V1 = A2V2, where A represents cross-sectional area and V represents fluid velocity.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation
  • Knowledge of the continuity equation for incompressible fluids
  • Familiarity with the concept of cross-sectional area in fluid flow
  • Basic algebra for solving equations involving fluid velocities
NEXT STEPS
  • Study the application of Bernoulli's equation in various fluid flow scenarios
  • Learn about the continuity equation and its implications for fluid dynamics
  • Explore the effects of viscosity on fluid flow in different pipe configurations
  • Investigate real-world applications of fluid dynamics in medical scenarios, such as blood flow in arteries
USEFUL FOR

Students studying fluid dynamics, engineers working on biomedical applications, and anyone interested in the principles of fluid flow in pipes.

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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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