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Week 3 - Pitot tube

1. Literature Review of Pitot - Static Tube It is a device that measures the stagnation pressure and static pressure of the fluid flow. The devices consists of a tube with two openings. One opening points directly into the fluid flow, while the other opening opens perpendicular to the fluid flow. It is commonly used to…

Dushyanth Srinivasan
updated on 15 Jun 2022

1. Literature Review of Pitot - Static Tube

It is a device that measures the stagnation pressure and static pressure of the fluid flow. The devices consists of a tube with two openings. One opening points directly into the fluid flow, while the other opening opens perpendicular to the fluid flow.

It is commonly used to measure the velocity of fluid in pipes, airplanes, etc.

The opening pointing into the fluid flow measures the stagnation pressure of the fluid. The opening perpendicular measures the static pressure.

The static pressure is pressure exerted by the fluid due to its weight (ex: atmospheric pressure), the stagnation pressure is the pressure when the velocity of the fluid is zero.

At stagnation pressure, the energy of the fluid is entirely due to static pressure and dynamic pressure (pressure exerted by moving fluid)

Stagnation pressure = static pressure + dynamic pressure

$P_{s t a g n a t i o n} = P_{s t a t i c} + P_{d y n a m i c}$ $P_(stagnation) = P_(static) + P_(dynamic)$

$P_{s t a g n a t i o n} - P_{s t a t i c} = ρ \cdot \frac{v^{2}}{2}$ $P_(stagnation) - P_(static) = rho*v^2/2$

In most pitot tubes, the pressure differential is calculated using a pressure transducer or manometer and the velocity is calculated from the following expression:

$v = \sqrt{\frac{2 (P_{s t a g n a t i o n} - P_{s t a t i c})}{ρ}}$ $v=sqrt ((2(P_(stagnation)-P_(static)))/rho)$

Note: Static Pressure is also referred to as Total Pressure.

2. Create surfaces and fill it separately for Total pressure port and static pressure port as shown below.

Inlet for total pressure

Inlet for static pressure

outlet for total pressure

outlet for total pressure (outer ring)

Note: File could not be processed properly since it is a .msh file and not a geometry file.

3. For the values of velocity given below calculate the total and static pressures and find the error in percentage for velocity.

Velocity(m/s)	Gauge Pressure (Pa)
240	-2817
100	33287
62	65780

Assuming 0 gauge pressure is atmospheric pressure (101325 Pa)

Static Pressure = Gauge Pressure + Atmospheric Pressure

Static Pressure = Gauge Pressure + 101325

Velocity(m/s)	Gauge Pressure (Pa)	Static Pressure (Pa)
240	-2817	98508
100	33287	134612
62	65780	167105

Total Pressure = static pressure + dynamic pressure

Dynamic Pressure = $\frac{ρ \cdot v^{2}}{2}$ $(rho*v^2)/2$

Assuming density for air at 300K as 1.225 $k g / m^{3}$ $kg//m^3$

Total Pressure = static pressure + $\frac{1.225 \cdot v^{2}}{2}$ $(1.225*v^2)/2$

Velocity(m/s)	Gauge Pressure (Pa)	Static Pressure (Pa)	Total Pressure (Pa)
240	-2817	98508	133788
100	33287	134612	140737
62	65780	167105	169459.45

fedgr

References

1. Chaos386, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons

2. https://www.grc.nasa.gov/www/k-12/airplane/pitot.html

Read more Projects by Dushyanth Srinivasan (45)

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Objective:

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Week 5 - Genetic Algorithm

Objective:

In this project, I will be generating a stalagmite function in MATLAB and find the global maxima of the function using Genetic Algorithm. A stalagmite function is a function which generates Stalactites, which are named after a natural phenomenon where rocks rise up from the floor of due to accumulation of droppings of…

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Week 4.1 - Solving second order ODEs

Objective:

In this project, I will be writing code in MATLAB to solve the motion of a simple pendulum. A simple pendulum motion's depends on Newton's Second Law. The equation which governs the motion of a simple pendulum is (with damping) $\frac{d^{2} θ}{{d t}^{2}} + \frac{b}{m} \frac{d θ}{d t} + \frac{g}{L} \sin θ = 0$ $(d^2theta)/(dt^2) + b/m(d theta)/(dt) + g/L sin theta = 0$ Where, $θ$ $theta$ is the angular displacement…