Pitot Static Tube Principle

A pitot static tube is a device used to measure the velocity of flow at a specific point in a fluid stream. It works on the principle of converting the kinetic energy of the flowing fluid into potential energy, measured as a pressure difference.

The tube has two openings: one facing the direction of flow (stagnation point) and another perpendicular to the flow (static pressure point). The difference in pressure measured between these two points is related to the velocity head of the fluid.

Given Data

We are given the following values:

• Stagnation pressure head ($\text{h}_s$) = 6 m
• Static pressure head ($\text{h}_a$) = 5 m
• Coefficient of the tube ($\text{C}_v$) = 0.98

The difference in pressure head, also known as the velocity head (h), is given by:

$\text{h} = \text{h}_s - \text{h}_a$

Let's calculate the velocity head.

Calculating Velocity Head

The difference in pressure heads is:

$\text{h} = 6 \text{ m} - 5 \text{ m} = 1 \text{ m}$

This pressure head difference corresponds to the velocity head.

Velocity Calculation using Pitot Tube

The theoretical velocity ($\text{V}_{th}$) of the fluid flow can be calculated using the Torricelli's theorem adapted for fluids, which relates velocity to the square root of the pressure head difference:

$\text{V}_{th} = \sqrt{2gh}$

where:

• g is the acceleration due to gravity (approximately 9.81 m/s²)
• h is the velocity head

However, a real pitot static tube has a coefficient of velocity ($\text{C}_v$) which accounts for the minor losses and non-ideal conditions. The actual velocity (V) is given by:

$\text{V} = \text{C}_v \times \sqrt{2gh}$

Step-by-Step Velocity Calculation

Now, let's plug in the values into the formula:

Given $\text{C}_v = 0.98$, g $\approx$ 9.81 m/s², and h = 1 m.

$\text{V} = 0.98 \times \sqrt{2 \times 9.81 \text{ m/s²} \times 1 \text{ m}}$

First, calculate the term inside the square root:

$2 \times 9.81 \times 1 = 19.62 \text{ m²/s²}$

Next, take the square root:

$\sqrt{19.62} \approx 4.429 \text{ m/s}$

Finally, multiply by the coefficient of velocity:

$\text{V} = 0.98 \times 4.429 \text{ m/s}$

$\text{V} \approx 4.34042 \text{ m/s}$

Result

The calculated velocity of flow is approximately 4.34 m/s.