# What Is the Angle of the Jet Before Deflection in Aerodynamics?

• Poppietje
In summary: N. Therefore, the adjacent side has a force of (120 - 0) N = 120 N. Since the area of the sphere is 4πr2, the total force on the sphere is (4π120 N) = 4.81 N.
Poppietje
Hello!
This is probably a rather simple problem, but I've been a bit confused about how to approach it. Any kick in the right direction for problem b) would be much appreciated! (Below is the full problem statement and sub-questions also for those who want to practice their physics. The question that I need help with is in bold.)

## Homework Statement

A sphere with a weight W = 20N "hangs" under a free homogeneous jet of air. The jet is deflected by the sphere, the original angle α changes to the horizontal. The velocity of the jet before deflection V1 = 20 m/s, the cross-sectional area before deflection A1 = 0.25m2. The air density ρ = 1.2 kg/m3.
Viscous forces on the sphere are neglected.

a) Choose a control volume and draw a vector diagram showing the relationship between the force on the jet and the momentum per second entering and leaving the control volume.
b) Calculate the angle α of the jet before deflection.
Calculate c) V2 and d) A2 of the jet after deflection.

## Homework Equations

At this point, all of our problems are to be solved using Bernoulli's equation, the Continuity equation and the Momentum equation. (Though I figure that the angle part is just pure trigonometry. :) )

## The Attempt at a Solution

For problem b):
My instinct would be to just take the tan-1 of the values opp./adj., as taught by trigonometry. Problem is, I have no idea how to define these values. I did calculate that the force of the flow at the inlet area is 120N assuming that the flow travels horizontally, giving us what could be used as the value for the adjacent side. I'm just not convinced of if this is the correct approach for solving for α, and even if it was, I'm not sure how to proceed with this information.

Any help would be greatly appreciated! Thank you!

Poppietje said:
Hello!
This is probably a rather simple problem, but I've been a bit confused about how to approach it. Any kick in the right direction for problem b) would be much appreciated! (Below is the full problem statement and sub-questions also for those who want to practice their physics. The question that I need help with is in bold.)

## Homework Statement

A sphere with a weight W = 20N "hangs" under a free homogeneous jet of air. The jet is deflected by the sphere, the original angle α changes to the horizontal. The velocity of the jet before deflection V1 = 20 m/s, the cross-sectional area before deflection A1 = 0.25m2. The air density ρ = 1.2 kg/m3.
Viscous forces on the sphere are neglected.

a) Choose a control volume and draw a vector diagram showing the relationship between the force on the jet and the momentum per second entering and leaving the control volume.
b) Calculate the angle α of the jet before deflection.
Calculate c) V2 and d) A2 of the jet after deflection.

## Homework Equations

At this point, all of our problems are to be solved using Bernoulli's equation, the Continuity equation and the Momentum equation. (Though I figure that the angle part is just pure trigonometry. :) )

## The Attempt at a Solution

For problem b):
My instinct would be to just take the tan-1 of the values opp./adj., as taught by trigonometry. Problem is, I have no idea how to define these values. I did calculate that the force of the flow at the inlet area is 120N assuming that the flow travels horizontally, giving us what could be used as the value for the adjacent side. I'm just not convinced of if this is the correct approach for solving for α, and even if it was, I'm not sure how to proceed with this information.

Any help would be greatly appreciated! Thank you!
Welcome to PF.

For that 120 N force you calculated -- there is a "Δv" involved in that calculation, since you are calculating Δpt. It appears that you have used 20 m/s for Δv. This would be the case if the air jet were brought to a complete stop:
Δv = (20 - 0) m/s ←(Note: NOT TRUE for this problem.)​
However, the jet is not brought to a stop, it is only deflected. So Δv is not the full 20 m/s initial speed of the jet. So, what is Δv in this case, in terms of the angle? Be aware that we are really just interested in one component of Δv (Question: vertical or horizontal?) here.

Part (a) calls for you to "choose a control volume and draw a vector diagram showing the relationship between the force on the jet and the momentum per second entering and leaving the control volume." So, let's see it. This diagram was asked for so it can help you solve the problem correctly.

Chet

## 1. What is aerodynamics?

Aerodynamics is the study of how air moves around objects. It is a branch of physics that deals with the motion of air and the forces that act on objects as they move through it.

## 2. What are some common beginner problems in aerodynamics?

Some common beginner problems in aerodynamics include understanding the concepts of lift and drag, calculating air resistance, and determining the best shape for an object to minimize drag.

## 3. How is aerodynamics important in everyday life?

Aerodynamics is important in everyday life because it helps us understand the behavior of objects in motion, such as airplanes, cars, and sports equipment. It also allows engineers to design more efficient and streamlined vehicles and structures.

## 4. What are some key principles of aerodynamics?

Some key principles of aerodynamics include Bernoulli's principle, which explains how air pressure changes as it moves over an object, and Newton's laws of motion, which describe the relationship between forces and motion.

## 5. How can I improve my understanding of aerodynamics as a beginner?

As a beginner, you can improve your understanding of aerodynamics by studying the basic principles and equations, practicing calculations and problem-solving, and conducting experiments or simulations to see how different factors affect aerodynamic forces. It may also be helpful to consult with more experienced scientists or engineers in the field.

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