Need the solution by the end of the day! Thank you! 2. If an incompressible laminar flow (through pipe area \(A_1\)) is forced through a narrow orifice, it will be focused into a smaller area, known as the *vena contracta* (with cross-sectional area \(A_2\)), as shown below:![Diagram](attachment) **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 pressures upstream (\(p_1\)) and downstream (\(p_2\)) from the orifice, the volumetric flow rate (\(Q\)) can be determined.(a) If the velocity of the fluid entering the pipe is \(u_1\), what is the velocity \(u_2\) at the end of the *vena contracta*?(b) What is the velocity of the fluid after the flow pattern has been reestablished?(c) What is the relationship between pressure drop (\(p_1 - p_2\)) and volumetric flow rate \(Q\)?---**Explanation of Diagram:**The diagram illustrates an orifice in a pipe with different sections labeled:- **Orifice area \(A_0\)**: The initial area of the pipe before the orifice.- **Flanges**: Segments around the orifice.- **Vena contracta area \(A_2\)**: The smaller area where the flow converges, resulting in increased velocity.- **Intense turbulence and loss of energy**: Turbulent flow occurs immediately after the *vena contracta*.- **Reestablished flow pattern**: The flow returns to a laminar state further downstream.- **Pressure tappings**: Areas where pressures \(p_1\) and \(p_2\) are measured.- **Eddies**: Circular flow patterns indicating turbulence.The flow is initially laminar, becomes turbulent through the orifice, and eventually returns to a laminar state.

Consider an incompressible laminar flow through pipe with orifice meter installed in it as shown in…

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 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?

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 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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