3. Air flows steadily through a pipe of circular cross-section shown below. At point 2, a tube connected to the pipe extends downward into a tub of water at rest. Air leaves the pipe at point 3 to the atmosphere. For the pipe, the cross-sectional areas A₁ = A3 > A2. Derive an expression for the height h to which water will rise in the vertical tube, as a function of the specific gravity of air (SG Pair Pwater), velocity at point 1 (V₁), pipe diameters at point 1 (D₁) and point 2 (D2), and any relevant constants. You may assume that air is incompressible and inviscid (thus, flow variables are all uniform at any cross-section). = Air in 1 2 3 Air out

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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3. Air flows steadily through a pipe of circular cross-section shown below. At point 2, a tube connected to the
pipe extends downward into a tub of water at rest. Air leaves the pipe at point 3 to the atmosphere. For the
pipe, the cross-sectional areas A₁ = A3 > A2. Derive an expression for the height h to which water will rise
in the vertical tube, as a function of the specific gravity of air (SG Pair Pwater), velocity at point 1 (V₁),
pipe diameters at point 1 (D₁) and point 2 (D2), and any relevant constants. You may assume that air is
incompressible and inviscid (thus, flow variables are all uniform at any cross-section).
=
Air in
1
2
3
Air out
Transcribed Image Text:3. Air flows steadily through a pipe of circular cross-section shown below. At point 2, a tube connected to the pipe extends downward into a tub of water at rest. Air leaves the pipe at point 3 to the atmosphere. For the pipe, the cross-sectional areas A₁ = A3 > A2. Derive an expression for the height h to which water will rise in the vertical tube, as a function of the specific gravity of air (SG Pair Pwater), velocity at point 1 (V₁), pipe diameters at point 1 (D₁) and point 2 (D2), and any relevant constants. You may assume that air is incompressible and inviscid (thus, flow variables are all uniform at any cross-section). = Air in 1 2 3 Air out
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