= One way to measure the drag force on an object is to measure the velocity profile in its wake. Any drag force will result in a reduction in the momentum of the fluid flowing around the object. This is the essence of conservation of momentum! Figure 4 shows an object in a flow with a free stream velocity of U 50m/s and you experimentally measure the x component of the velocity in the wake of the object as u = 35+252 within the range of 0 m < r < 1 m. The control volume you use to analyze this flow is shown in Red lines in the figure: the outside surface of the CV follows streamlines and the front (H) has a diameter of 3 m. It looks like a cylinder that gets wider as you go to the right. If the density of the fluid is 1.23kg/m³, answer the following: (a) Explain in words why using a streamline for the top and bottom of the control volume allows us to know that the mass flux across those surfaces is zero. (b) Given that the mass flux across the streamlines is zero, find the radius of the control volume on the right hand side. i.e. determine R2. Hint: You will need to perform ring integration. [1.45 - 1.55 m] (c) Determine the drag force on the object in the flow. Hint: You can not solve for the drag force directly, instead you need to add a force to the object that holds it in place. This will be equal but opposite to the drag force. [240 - 325 N] H 230 Velocity profile measured here R₂ wahe area }u=0 U=35+251² }u.σ и
= One way to measure the drag force on an object is to measure the velocity profile in its wake. Any drag force will result in a reduction in the momentum of the fluid flowing around the object. This is the essence of conservation of momentum! Figure 4 shows an object in a flow with a free stream velocity of U 50m/s and you experimentally measure the x component of the velocity in the wake of the object as u = 35+252 within the range of 0 m < r < 1 m. The control volume you use to analyze this flow is shown in Red lines in the figure: the outside surface of the CV follows streamlines and the front (H) has a diameter of 3 m. It looks like a cylinder that gets wider as you go to the right. If the density of the fluid is 1.23kg/m³, answer the following: (a) Explain in words why using a streamline for the top and bottom of the control volume allows us to know that the mass flux across those surfaces is zero. (b) Given that the mass flux across the streamlines is zero, find the radius of the control volume on the right hand side. i.e. determine R2. Hint: You will need to perform ring integration. [1.45 - 1.55 m] (c) Determine the drag force on the object in the flow. Hint: You can not solve for the drag force directly, instead you need to add a force to the object that holds it in place. This will be equal but opposite to the drag force. [240 - 325 N] H 230 Velocity profile measured here R₂ wahe area }u=0 U=35+251² }u.σ и
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.70P
Related questions
Question
![=
One way to measure the drag force on an object is to measure the velocity profile in its wake. Any drag force will
result in a reduction in the momentum of the fluid flowing around the object. This is the essence of conservation of
momentum! Figure 4 shows an object in a flow with a free stream velocity of U 50m/s and you experimentally
measure the x component of the velocity in the wake of the object as u = 35+252 within the range of 0 m < r < 1 m.
The control volume you use to analyze this flow is shown in Red lines in the figure: the outside surface of the CV
follows streamlines and the front (H) has a diameter of 3 m. It looks like a cylinder that gets wider as you go to the
right. If the density of the fluid is 1.23kg/m³, answer the following:
(a) Explain in words why using a streamline for the top and bottom of the control volume allows us to know that the
mass flux across those surfaces is zero.
(b) Given that the mass flux across the streamlines is zero, find the radius of the control volume on the right hand
side. i.e. determine R2. Hint: You will need to perform ring integration. [1.45 - 1.55 m]
(c) Determine the drag force on the object in the flow. Hint: You can not solve for the drag force directly, instead
you need to add a force to the object that holds it in place. This will be equal but opposite to the drag force. [240
- 325 N]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d69634b-8a8a-4609-8704-3bdadaefe256%2Fb5780fa5-bb73-4507-9f44-dd5de8b850cb%2F18fiu2h_processed.png&w=3840&q=75)
Transcribed Image Text:=
One way to measure the drag force on an object is to measure the velocity profile in its wake. Any drag force will
result in a reduction in the momentum of the fluid flowing around the object. This is the essence of conservation of
momentum! Figure 4 shows an object in a flow with a free stream velocity of U 50m/s and you experimentally
measure the x component of the velocity in the wake of the object as u = 35+252 within the range of 0 m < r < 1 m.
The control volume you use to analyze this flow is shown in Red lines in the figure: the outside surface of the CV
follows streamlines and the front (H) has a diameter of 3 m. It looks like a cylinder that gets wider as you go to the
right. If the density of the fluid is 1.23kg/m³, answer the following:
(a) Explain in words why using a streamline for the top and bottom of the control volume allows us to know that the
mass flux across those surfaces is zero.
(b) Given that the mass flux across the streamlines is zero, find the radius of the control volume on the right hand
side. i.e. determine R2. Hint: You will need to perform ring integration. [1.45 - 1.55 m]
(c) Determine the drag force on the object in the flow. Hint: You can not solve for the drag force directly, instead
you need to add a force to the object that holds it in place. This will be equal but opposite to the drag force. [240
- 325 N]
Transcribed Image Text:H
230
Velocity profile
measured
here
R₂
wahe
area
}u=0
U=35+251²
}u.σ
и
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