f10_fall - Fluids – Lecture 10 Notes 1 Substantial...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fluids – Lecture 10 Notes 1. Substantial Derivative 2. Recast Governing Equations Reading: Anderson 2.9, 2.10 Substantial Derivative Sensed rates of change The rate of change reported by a flow sensor clearly depends on the motion of the sensor. For example, the pressure reported by a static-pressure sensor mounted on an airplane in level flight shows zero rate of change. But a ground pressure sensor reports a nonzero rate as the airplane rapidly flies by a few meters overhead. The figure illustrates the situation. p (t) 1 p (t) 2 o t = t wing location at o t p (t) 1 p (t) 2 p t Note that although the two sensors measure the same instantaneous static pressure at the same point (at time t = t o ), the measured time rates are different. dp 1 dp 2 p 1 ( t o ) = p 2 ( t o ) but ( t o ) negationslash = ( t o ) dt dt Drifting sensor We will now imagine a sensor drifting with a fluid element . In effect, the sensor follows the element’s pathline coordinates x s ( t ), y s ( t ), z s ( t ), whose time rates of change are just the local flow velocity components dx s dy s dz s = u ( x s , y s , z s , t ) , = v ( x s , y s , z s , t ) , = w ( x s , y s , z s , t ) dt dt dt V p (t) s s p pathline pressure field sensor drifting with local velocity s Dp dp Dt dt t Consider a flow field quantity to be observed by the drifting sensor, such as the static pressure...
View Full Document

This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

Page1 / 3

f10_fall - Fluids – Lecture 10 Notes 1 Substantial...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online