1 / 14

6 . Property Balance Math + Mass balances

6 . Property Balance Math + Mass balances. CH EN 374: Fluid Mechanics. Review: Material Derivative. H ow f changes for a fluid particle. H ow f changes in each direction. H ow a fluid particle moves through the field. H ow the field itself changes with time. Example from the Homework….

phurst
Télécharger la présentation

6 . Property Balance Math + Mass balances

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6. Property Balance Math + Mass balances CH EN 374: Fluid Mechanics

  2. Review: Material Derivative How f changes for a fluid particle How f changes in each direction How a fluid particle moves through the field How the field itself changes with time

  3. Example from the Homework…

  4. Overall Change for Control Volume • Take an extensive property B • Examples: mass, momentum, energy • Overall change inside control volume: • Affected by: • Change inside CV • Flow in and out Control Volume

  5. Reynold’s Transport Theory (RTT) • How is this similar to the material derivative? • Gives a macroscopic or integral material balance Total change of property Change within the control volume. Flow in and out across the control surface. Control Volume Control Surface

  6. Change of B inside control volume. • What will make this term change with time? • Density changing • Control volume changing shape or size

  7. Flow in and out of control volume. • is a vector normal to the control surface at any point • is the velocity component normal to surface—that’s what goes in or out

  8. vavg A • For each inlet and outlet: • For the total, add together inlets and outlets

  9. Simplification • In this class we will only use RTT for: • Incompressible flows • Fixed control volumes • How does this simplify the equation? Control Volume Control Surface

  10. What did I want you to get out of all that? • Be able to describe what each term in the RTT means • Know the assumptions that go into simple material balances • Now we turn this into balances for different properties. • Today: Mass • Monday: Momentum • Wednesday: Mechanical Energy

  11. Conservation of Mass • Mass: • What’s B? • What’s b? • What’s dB/dt? • What’s ?

  12. Conservation of Mass

  13. Problem • A desktop computer is to be cooled by a fan whose flow rate is 0.40 m3/min. Determine the mass flow rate of air through the fan at an elevation of 3400 m where the air density is 0.7 kg/m3.

  14. Problem • A cylindrical water tank of radius whose top is open to the atmosphere is initially filled with water to a height of . A discharge plug near the bottom of the tank is pulled out and water begins to drain through a circular hole of diameter . • If we assume that energy losses through the hole at the bottom of the tank are negligible, the average velocity of the exiting water is given by , where is gravitational acceleration and is the height of water in the tank (this will be a function of time. This is called Toricelli’s Law and we will derive it ourselves next week. • Determine • If is 3 ft, is 4 ft, and is 0.5 in, how long will it take for the water level in the tank to drop to 2 ft?

More Related