Applications — Pitot tube, Venturi meter, orifice flow: Foundations

Before you can trust the Pitot / Venturi / Orifice formulas, you must be able to read them. Below is every symbol and idea the parent note leans on, built from nothing, each one earning the next.

1. Fluid, streamline, and "a particle of fluid"

Why the topic needs it: every derivation says "point 1 ... point 2 ... along a streamline." That phrase means: pick one blob and watch it travel from the wide pipe to the throat, or from the tank surface to the hole. Without the streamline picture, the equation is just symbols.

2. Density $ρ$ — how heavy the stuff is

Why the topic needs it: energy in a fluid is bookkept per unit volume, and to turn "how fast" into "how much energy" you must know how much mass sits in each volume — that is exactly $ρ$ . It is why a Pitot tube gives a different speed in air vs water for the same push.

3. Pressure $P$ — the push per area

Why the topic needs it: all three devices measure a pressure difference $P_{1} - P_{2}$ and convert it to a speed. Pressure is the quantity the tubes actually sense.

4. Speed $v$ and area $A$

Picture slicing the pipe with a knife perpendicular to the flow — the face you expose is $A$ .

5. Volume flow rate $Q$ and Continuity

Why the topic needs it: Continuity Equation gives the second equation (besides Bernoulli) that lets us eliminate one unknown speed and solve for the other.

6. Height $h$ and $g$ — the gravity term

Why the topic needs it: the $ρ g h$ term drives Torricelli's draining tank. In a horizontal Pitot or Venturi, $h_{1} = h_{2}$ so this term simply cancels.

7. The three energies of Bernoulli, in one line

$\frac{1}{2} ρ v^{2}$ is called the dynamic pressure — the "cost" of moving.
$P$ (the ordinary sensed push) is the static pressure.
$P + \frac{1}{2} ρ v^{2}$ (what a face-on tube reads when it stops the flow) is the stagnation pressure.

See Dynamic vs Static vs Stagnation Pressure for these three names, and Bernoulli's Equation for the full derivation.

The path a single fluid particle follows as it flows.

Units and meaning of density

ρ

Mass per unit volume,

kg/m^{3}

Why does pressure push equally in all directions?

In a fluid at a point there is no preferred direction; force per area is the same every way.

Convert

5 cm^{2}

to SI.

5 \times 1 0^{- 4} m^{2}

State continuity in words.

The same volume per second crosses every cross-section, so narrow means fast.

Why does the kinetic term carry a factor

\frac{1}{2}

Kinetic energy is

\frac{1}{2} m v^{2}

; per volume,

m \to ρ

, giving

\frac{1}{2} ρ v^{2}

What are the units of every term in Bernoulli?

Pascals — energy per unit volume.

How does a manometer turn a pressure difference into something readable?

P_{1} - P_{2} = ρ_{m} g Δ h

— the difference lifts a liquid column of height

Δ h

Δ P

doubles, how does speed change?

It grows by

2 \approx 1.41

, since

v \propto Δ P

Foundations — Applications — Pitot tube, Venturi meter, orifice flow

1. Fluid, streamline, and "a particle of fluid"

2. Density $ρ$ — how heavy the stuff is

3. Pressure $P$ — the push per area

4. Speed $v$ and area $A$

5. Volume flow rate $Q$ and Continuity

6. Height $h$ and $g$ — the gravity term

7. The three energies of Bernoulli, in one line

8. The manometer link: $Δ P = ρ_{m} g Δ h$

9. Prerequisite map

Equipment checklist