RTT – Αρχή διατήρησης της Ορμής

Image taken from: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node19.html

The RTT in Mathematical Terms

CONTROL VOLUME SYSTEM

1) If BSYS is a physical Property of the System

2) And b = BSYS /MSYS (where MSYS is the mass of the system)

Volume Integral Surface Integral

RTT & the Conservation of Mass Let BSYS = MSYS (the mass of the system) then b = 1

RTT – Conservation of Mass

RTT & the Conservation of Momentum Let BSYS = 𝑷𝑺𝑺𝑺 (the Linear Momentum of the System)

In this case: 𝒃 = 𝑷𝑺𝑺𝑺/ MSYS = 𝑽 (velocity )

BSYS = 𝑷𝑺𝑺𝑺 = ∫ 𝑉 𝜌 𝑑𝑉𝑆𝑆𝑆

Conservation of Momentum

In component Form

Example 1: Water Jet Hitting a flat, vertical plate

1) What is V’? 2) What is Rx? (the force in the x-direction that is applied to the plate)

Step 1: Define the Control Volume You want V’ and Rx to appear in the Control Surface (CS)

Step 2:

Step 3: Conversation of Momentum (x-direction)

∑𝑭𝑿 = 𝝏𝝏𝝏 ∫ 𝑽𝑿 𝝆 𝒅𝑽𝑪𝑽 + ∫ 𝑽𝑿 𝝆𝑪𝑺 (𝑽 ∙ 𝒏) dA

Example 2: Steady Flow through a 1800 bent

Step 1: Define you Control Volume (CV) -is this a steady-state problem? -should you include the anchor in the CV?

Absolute Pressure

In the kitchen

Step 2: Conservation of Mass

Step 3: Conservation of Momentum X-direction:

Y-direction:

Absolute or Gauge Pressure?

Example 3: Discharging Water from a Tank

Step 1: Define the CV

Fixed Not Fixed (?)

The rest on the board…

A: the area at the bottom of the tank