Fluid Mechanics: pitot static tube/manometer system

[ywkim880801]

Homework Statement

A water-filled manometer is connected to a Pitot-static tube to measure a nominal airspeed of 50 ft/s. It is assumed that a change in the manometer reading of 0.002 in. can be detected. What is the minimum deviation from the 50 ft/s airspeed that can be detected by this system?

Homework Equations

velocity measurement for a pitot-static tube

V=$$\sqrt{}2(p3-p4)/\rho$$


please help me!
honestly, I don't even understand what the question is asking

 

[Valkarie]

. The equation you have given me is for measuring velocity using a Pitot-static tube, but I don't understand how to use it to answer this question.

 

[Mene]

.

I would first clarify the question and make sure I understand the context and assumptions being made. From my understanding, the question is asking for the minimum deviation in airspeed that can be detected by the given Pitot-static tube/manometer system.

To answer this, we can use the equation for velocity measurement using a Pitot-static tube, which is V = √(2*(p3-p4)/ρ), where p3 is the stagnation pressure and p4 is the static pressure. The density of air, ρ, is assumed to be constant.

Since we want to find the minimum deviation in airspeed, we can rearrange the equation to solve for the difference between p3 and p4, which is equivalent to the change in manometer reading, Δp = p3 - p4. This gives us the equation Δp = ρ*V^2/2.

We are given that the change in manometer reading that can be detected is 0.002 in. We can convert this to the corresponding change in pressure using the equation Δp = ρ*g*h, where g is the acceleration due to gravity and h is the change in manometer reading in inches. Substituting in the given values, we get Δp = (1.225 kg/m^3)*(9.8 m/s^2)*(0.002 in)*(0.0254 m/in) = 0.0000601 kg/m*s^2.

Now, we can solve for the minimum deviation in airspeed by substituting this value into the equation Δp = ρ*V^2/2. This gives us V = √(2*(0.0000601 kg/m*s^2)/1.225 kg/m^3) = 0.00591 m/s.

Therefore, the minimum deviation in airspeed that can be detected by this system is 0.00591 m/s or approximately 0.02 ft/s.

I hope this helps clarify the question and provides a solution to the problem. It is important to note that this is a theoretical calculation and the actual minimum detectable deviation may vary in real-world applications due to various factors such as instrument precision and environmental conditions.