PHYSICS 3K03 Lecture Notes - Lecture 8: Conservation Of Mass, Reynolds Transport Theorem

Hi there, I was wondering if you could help me with the followingquestions.

1. Will a fluid reach equilibrium when subjected to a steady statestress?
2. Does the distribution of shear stress for lamina flow, varyparabolically with the radius of the pipe?
3. Is the Reynolds number a measure of the ratios of the inertialforces to the viscous forces?
4. If the width is D and breath is 3D, is the hydraulic diameter ofthe full rectangular pipe 2D?
5. Is a friction factor a dimensionless wall shear stress?
6. For laminar flow in a horizontal pipe, under a constant pressuregradient, doe the doubling of the diameter result in a doubling ofthe flow rate?
7. For a rough pipe, does the friction factor keep on decreasingwhen the Reynolds number increases?
8. For a given volumetric flow rate, Q, is the pressure drop inturbulent flow approx. proportional to 1/(D^5) where D= diameter,?

Thanks,
Rebecca

A16. A child of mass 50.0 kg stands 2.00 m from the center ofa
horizontal circular disc of radius 4.00 m and mass 200 kg. The discis
mounted on a frictionless, vertical axis. Initially both the childand the
disc are at rest. (Hint: so what is their combined initialangular
momentum?) The child then begins to run in a counterclockwise
direction. Shortly after the child starts running, it is observedthat the
disc attains a steady angular velocity of w= - 0.125rad/s ina
clockwise sense. The moment of inertia of the flat disc is givenby:
I = 1/2 mR^2
(i) Calculate the angular momentum of the disc (NOT the child)about the central vertical axis when the child has reached
its steady (constant) tangential speed.
(ii) Calculate the steady tangential speed at which the child isrunning

Air enters a horizontal, constant-diameter heating duct operating at a 2 steady state at 290 K, 1 bar, with a volumetric flow rate of 0.25 m³/s, and exits at 325 K, 0.95 bar. The flow area is 0.04 m². Assuming the ideal gas model with k 5 1.4 for the air, determine

(a) the mass flow rate, in kg/s,

(b) the velocity at the inlet and exit, each in m/s, and

(c) the rate of heat transfer, in kW.