If an incompressible laminar flow (through pipe area A₁) is forced through a narrow orifice, it will be focused into a smaller area, known as the vena contracta (with cross-sectional area A₂), as shown below: Orifice area Ao A₁ P₁ Flanges Pipe wall P2 Vena con- tracta area A₂ Eddies Intense turbulence and loss of energy Pressure tappings Reestablished flow pattern Figure 3: Flow through an orifice. The orifice focuses the laminar flow to a vena contracta, increasing its velocity. Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pres- sures upstream (p₁) and downstream (p2) from the orifice, the vol- umetric flow rate (Q) can be determined. (a) If the velocity of the fluid entering the pipe is u₁, what is the velocity u2 at the end of the vena contracta? (b) What is the velocity of the fluid after the flow pattern has been reestablised? (c) What is the relationship between pressure drop (p₁ - p2) and volumetric flow rate Q?

If an incompressible laminar flow (through pipe area A₁) is forced through a narrow orifice, it will be focused into a smaller area, known as the vena contracta (with cross-sectional area A₂), as shown below: Orifice area Ao A₁ P₁ Flanges Pipe wall P2 Vena con- tracta area A₂ Eddies Intense turbulence and loss of energy Pressure tappings Reestablished flow pattern Figure 3: Flow through an orifice. The orifice focuses the laminar flow to a vena contracta, increasing its velocity. Beyond the orifice, the flow becomes turbulent for some distance until a laminar flow pattern is re-established. By measuring pres- sures upstream (p₁) and downstream (p2) from the orifice, the vol- umetric flow rate (Q) can be determined. (a) If the velocity of the fluid entering the pipe is u₁, what is the velocity u2 at the end of the vena contracta? (b) What is the velocity of the fluid after the flow pattern has been reestablised? (c) What is the relationship between pressure drop (p₁ - p2) and volumetric flow rate Q?

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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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

2. If an incompressible laminar flow (through pipe area A₁) is forced
through a narrow orifice, it will be focused into a smaller area,
known as the vena contracta (with cross-sectional area A₂), as
shown below:
Orifice
area Ao.
A₁
Flanges
Pipe wall
P₁
Vena con-
tracta area A₂
5/4
P2
Eddies
Intense turbulence
and loss of energy
Pressure
tappings
Reestablished
flow pattern
Figure 3: Flow through an orifice. The orifice
focuses the laminar flow to a vena contracta,
increasing its velocity.
Beyond the orifice, the flow becomes turbulent for some distance
until a laminar flow pattern is re-established. By measuring pres-
sures upstream (p₁) and downstream (p2) from the orifice, the vol-
umetric flow rate (Q) can be determined.
(a) If the velocity of the fluid entering the pipe is u₁, what is the
velocity u₂ at the end of the vena contracta?
(b) What is the velocity of the fluid after the flow pattern has been
reestablised?
(c) What is the relationship between pressure drop (p₁ - p₂) and
volumetric flow rate Q?

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