rtt – conversation of momentum · let . b. sys = 𝑷. 𝑺𝑺𝑺 (the linear momentum of the...
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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