Speed of water flowing through pipe

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Homework Help Overview

The problem involves calculating the volume flow rate of water in a piping system, specifically focusing on a section with a 4-inch diameter where the water flows at a speed of 3.0 ft/s. The context is fluid dynamics, particularly the principles of flow rate and area in relation to pipe diameter.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between flow rate, pipe area, and velocity, with one participant expressing uncertainty about how to begin the problem. Others suggest using the formula for flow rate and consider the implications of incompressible flow.

Discussion Status

The discussion is ongoing, with some participants providing guidance on the relevant equations and principles. There is an exploration of how flow rates remain constant across different pipe diameters, and questions are raised about the relationship between flow rate and velocity in varying pipe sections.

Contextual Notes

Participants note the assumption of incompressibility for water and the lack of a second density value. There is also a mention of a second part to the problem that requires finding the speed of water in a different diameter section.

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Homework Statement


The speed of water flowing through the "influent" 4-inch diameter section of the piping system below is 3.0 ft/s. What is the volume flow rate of water in the piping system? Express the volume flow rate in ft^3/s


Homework Equations





The Attempt at a Solution


I really don't know what to do. I know pi*r^2 comes into play here, but I need help. Just tell me how to start and guide me through it please.
2012-11-07%252021.12.49.jpg
 
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Flow rate = area of the pipe multiplied by the velocity.

You have everything but the flow rate. The area of the pipe is pi*r^2 as you said. Since you're not given a second density we can assume the flow is incompressible, and due to the conservation of mass, the flow rate in the 3 in dimater pipe will be the same. Q1 = Q2. I can't give you anymore without solving it for you.
 
Given that the fluid is water, it's safe to assume that the fluid is incompressible.
 
Vadar2012 said:
... the flow rate in the 3 in dimater pipe will be the same. Q1 = Q2.
Can the speed of the water be different even though the flow rate is the same? Part two says to find the speed of the water in the 3-inch diameter section in ft/s
 
Yes.
 
thatshowifeel said:
Can the speed of the water be different even though the flow rate is the same? Part two says to find the speed of the water in the 3-inch diameter section in ft/s

Yes, this is connected to the equation given by vadar2012: flow rate = area x velocity.
The flow rates are the same everywhere in the pipe (it must be, the water doesn't disappear). Therefore, if the area of the pipe increases, the velocity decreases.

So:
step 1: calculate flow rate = area x velocity or Q1=A1 x V1
step 2: use Q1 = Q2 to calculate V2
 

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