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A small irregularly-shaped object is being tested in a wind tunnel with a rectangular cross section (H=0.5 m tall and b=1 m deep). The object is two-dimensional in the sense that it extends through the depth of the wind tunnel with the same cross- sectional shape. The object is held in place with a slender support. The pressure is uniform across sections 1 and 2 of the wind tunnel. The upstream pressure is 145 Pa (gage) and the downstream pressure is 100 Pa (gage). The uniform velocity Vo at section 1 is 9 m/s. The velocity profile behind the object is deformed by the object's presence and the velocity profile is measured to be: U2 (Y) = { Assume that you can neglect viscous effects at the wind tunnel walls and that the properties of the air in the wind tunnel are constant (p = 1.20 kg/m³, µ = 1.80x10-5 kg/m s) Y X Y Y≥0 Vmax H/2 -Vmax H/2y<0 1 Vo V₁ u₂(y) d (₁₂ pav) + [₂p(ï ñ)dA=0 (Lov • dt max (2) For reference, conservation of mass and momentum for a control volume are given by: d ΣF = 1 / (√₁₂ põdv) + [₂ põ(v - ñ)dA ΣΕ dt H

A small irregularly-shaped object is being tested in a wind tunnel with a rectangular cross section (H=0.5 m tall and b=1 m deep). The object is two-dimensional in the sense that it extends through the depth of the wind tunnel with the same cross- sectional shape. The object is held in place with a slender support. The pressure is uniform across sections 1 and 2 of the wind tunnel. The upstream pressure is 145 Pa (gage) and the downstream pressure is 100 Pa (gage). The uniform velocity Vo at section 1 is 9 m/s. The velocity profile behind the object is deformed by the object's presence and the velocity profile is measured to be: U2 (Y) = { Assume that you can neglect viscous effects at the wind tunnel walls and that the properties of the air in the wind tunnel are constant (p = 1.20 kg/m³, µ = 1.80x10-5 kg/m s) Y X Y Y≥0 Vmax H/2 -Vmax H/2y<0 1 Vo V₁ u₂(y) d (₁₂ pav) + [₂p(ï ñ)dA=0 (Lov • dt max (2) For reference, conservation of mass and momentum for a control volume are given by: d ΣF = 1 / (√₁₂ põdv) + [₂ põ(v - ñ)dA ΣΕ dt H

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please sketch an appropriate control volume in relation to the wind tunnel. Identify all forces acting on the control volume that you draw.

a) Determine the mass flow rate through the wind tunnel (in kg/s).

b) Calculate Vmax (in m/s).

c) Find the drag force acting on the body (in N).

d) In which direction does the drag force act on the object?

A small irregularly-shaped object is being tested in a wind tunnel with a rectangular cross section (H=0.5 m tall and b=1 m deep). The object is two-dimensional in the sense that it extends through the depth of the wind tunnel with the same cross- sectional shape. The object is held in place with a slender support. The pressure is uniform across sections 1 and 2 of the wind tunnel. The upstream pressure is 145 Pa (gage) and the downstream pressure is 100 Pa (gage). The uniform velocity Vo at section 1 is 9 m/s. The velocity profile behind the object is deformed by the object's presence and the velocity profile is measured to be: U2 (Y) = { Assume that you can neglect viscous effects at the wind tunnel walls and that the properties of the air in the wind tunnel are constant (p = 1.20 kg/m³, µ = 1.80x10-5 kg/m s) Y X Y Y≥0 Vmax H/2 -Vmax H/2y<0 1 Vo V₁ u₂(y) d (₁₂ pav) + [₂p(ï ñ)dA=0 (Lov • dt max (2) For reference, conservation of mass and momentum for a control volume are given by: d ΣF = 1 / (√₁₂ põdv) + [₂ põ(v - ñ)dA ΣΕ dt H
Transcribed Image Text:A small irregularly-shaped object is being tested in a wind tunnel with a rectangular cross section (H=0.5 m tall and b=1 m deep). The object is two-dimensional in the sense that it extends through the depth of the wind tunnel with the same cross- sectional shape. The object is held in place with a slender support. The pressure is uniform across sections 1 and 2 of the wind tunnel. The upstream pressure is 145 Pa (gage) and the downstream pressure is 100 Pa (gage). The uniform velocity Vo at section 1 is 9 m/s. The velocity profile behind the object is deformed by the object's presence and the velocity profile is measured to be: U2 (Y) = { Assume that you can neglect viscous effects at the wind tunnel walls and that the properties of the air in the wind tunnel are constant (p = 1.20 kg/m³, µ = 1.80x10-5 kg/m s) Y X Y Y≥0 Vmax H/2 -Vmax H/2y<0 1 Vo V₁ u₂(y) d (₁₂ pav) + [₂p(ï ñ)dA=0 (Lov • dt max (2) For reference, conservation of mass and momentum for a control volume are given by: d ΣF = 1 / (√₁₂ põdv) + [₂ põ(v - ñ)dA ΣΕ dt H
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