1:

METR 3113: Atmospheric Dynamics 1

The Continuity Equation andthe Venturi Tube

Lecture for Monday, November 5, 2007

Prof. Brian H. Fiedler

School of Meteorology, University of Oklahoma

2:

A1 A2

x1

x2

Volume conservation of an incompressible flow through a

constriction. The volume vacated must be equal to the vol-

ume moved into:

A1x1 = A2x2

A1x1t

= A2x2t

A1u1 = A2u2

3:

A1u1 = A2u2

is one form of an incompressible continuity equation. The

fluid must remain continuous, no gaps are allowed to

form. Volume of all parcels must be conserved.

When you learn to do dynamics with a velocity field

~U(x, y, x, t), you will learn the incompressibility is

enforced by:

~U = 0

4: u1

u2

u212+

p1=

u222+

p2

p1 p2 = u212

A21A22

u21

2

p1 p2 = u212

(A21A22

1)

5:

p1 p2 = u212

(A21A22

1)

Knowledge of p1 p2 can be used to determine u1, andhence the volume flow rate u1A1 and mass flow rate

u1A1.

6:

Pitot-tube:

u212+

p1=

p2

1 is the static tap at the

side.

2 is the stagnation point at

the front.

7:

From Wikipedia Venturi Effect:

What is wrong with this picture?

Is p1 p2 proportional to h?