Question

Question: A pitot tube (Figure) on a high-altitude aircraft measures a differential pressure of $180Pa$. What is the aircraft’s airspeed if the density of the air is $0.031kg/m^3$?

Short answer

The plane’s airspeed is $1.1*{10}^{2}m/s$.

Step-By-Step Solution

Step 2: Determining the concept of Bernoulli’s equation

Find the expression for the plane's airspeed using Bernoulli's equation. Find the plane's airspeed using the supplied values and this phrase. According to Bernoulli's equation, the pressure inside a flowing fluid falls as the fluid's speed rises.

The formula is as follows:

role="math" localid="1657558198830" $pv+1/2p{g}^{2^{}}h+cons\tan t$

Where, $p$is pressure, v is velocity, h is height, $g$is the acceleration due to gravity, h is height, and $p$is density.

Step 3: Determining the plane’s airspeed

Determining the plane’s airspeed

Step-by-step solution

 Given information 

1. The pressure difference measured by the pitot tube is .

2. The density of air

Determining the concept of Bernoulli’s equation

Find the expression for the plane's airspeed using Bernoulli's equation. Find the plane's airspeed using the supplied values and this phrase. According to Bernoulli's equation, the pressure inside a flowing fluid falls as the fluid's speed rises.

The formula is as follows:

Where,is pressure, v is velocity, h is height, is the acceleration due to gravity, h is height, and is density.

Determining the plane’s airspeed 

The airflow obeys Bernoulli’s principle.

So,

Thus, rearranging,

Hence, the plane’s airspeed is .$1.1*{10}^{2}m/s$