Poiseuille’s law [Eq. (9-41)] gives the volume flow rate of a viscous fluid through a pipe, (a) Show that Poiseuille’s law can be written in the form ΔP = IR, where I = ΔV/Δt represents the volume flow rate and R is a constant of proportionality called the fluid flow resistance. (b) Find R in terms of the viscosity of the fluid and the length and radius of the pipe. (c) If two or more pipes are connected in series so that the volume flow rate through them is the same, do the resistances of the pipes add as for electrical resistors
(a)
Show that Poiseuille’s law can be written in the form
Answer to Problem 140P
It is shown that the Poiseuille’s law can be written in the form
Explanation of Solution
Write the expression for the volume flow rate.
Here,
Write the expression for the Poiseuille’s law.
Here,
Equate equation (I) and (II) to solve for
Conclusion:
Therefore, it is showed that the Poiseuille’s law can be written in the form
(b)
The constant of proportionality
Answer to Problem 140P
The constant of proportionality
Explanation of Solution
Write the expression for the driving pressure.
Equate equation (III) and (IV) to solve for
Conclusion:
Therefore, the constant of proportionality
(c)
Whether the resistance of the pipes add as for electrical resistors for pipes connected in series.
Answer to Problem 140P
Yes, the resistance of the pipes add as for electrical resistors.
Explanation of Solution
If two or more pipes are connected in series, the volume flow rate remains same.
Here,
Write the expression for the total driving pressure.
Here,
Use equation (VI) and (IV) in (VII) to solve for the
Write the expression electrical resistance for the series combination of resistors.
Use equation (IX) in (VIII) to solve for
Conclusion:
Therefore, the resistance of the pipes add as for electrical resistors.
(d)
Whether the resistance of the pipes add as for electrical resistors for pipes connected in parallel.
Answer to Problem 140P
Yes, the resistance of the pipes add as for electrical resistors for pipes connected in parallel.
Explanation of Solution
If two or more pipes are connected as parallel, the driving pressure drops across all the pipes are the same.
Use equation (IV) to solve for
Here,
Write the expression for the electrical resistance for parallel combination.
Use equation (XII) in (XI) to solve for
Conclusion:
Therefore, the resistance of the pipes add as for electrical resistors for pipes connected in parallel.
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Chapter 18 Solutions
Physics
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