Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Additional Documents & Tests for Civil Engineering (CE) > Analysis of Inviscid, Incompressible, Irrotational Flows (Part - 2)
Analysis of Inviscid, Incompressible, Irrotational Flows (Part - 2) | Additional Documents & Tests for Civil Engineering (CE) PDF Download
Source or Sink
Source flow -
A flow with straight streamlines emerging from a point.
Velocity along each streamline varies inversely with distance from the point (shown in Fig. 20.3).
Only the radial component of velocity is non-trivial. (vθ=0, vz=0 ).
In a steady source flow the amount of fluid crossing any given cylindrical surface of radius r and unit length is constant 
(20.10a)
(which shows that velocity is inversely proportional to the distance )
where, K is the source strength 
is the volume flow rate
The definition of stream function in cylindrical polar coordinate states that
(20.11)
For the source flow,
(20.13)
Combining Eqs (20 .12) and (20.13) , we get
(20.14)
Thus
Because the flow is irrotational, we can write
(20.15)
The integration constants C1 and C2 in Eqs (20.14) and (20.15) have no effect on the basic structure of velocity and pressure in the flow.
The equations for streamlines and velocity potential lines for source flow become
(20.16)
K = source strength and is proportional to   the rate of volume flow from the source per unit depth perpendicular to the page |
Sink flow
When
is negative , we get sink flow,here the flow is in the opposite direction of the source flow.
is negative , we get sink flow,
In Fig. 20.3, the point 0 is the origin of the radial streamlines. We visualize that point O is a point source or sink that induces radial flow in the neighbourhood .
The point source or sink is a point of singularity in the flow field (because vr becomes infinite).
The stream function and velocity potential function are
(20.17)
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FAQs on Analysis of Inviscid, Incompressible, Irrotational Flows (Part - 2) - Additional Documents & Tests for Civil Engineering (CE)
| 1. What are the assumptions made in analyzing inviscid, incompressible, irrotational flows? |  |
Ans. The assumptions made in analyzing inviscid, incompressible, irrotational flows are that the flow is frictionless (inviscid), the fluid has a constant density (incompressible), and the fluid particles do not rotate (irrotational). These assumptions simplify the mathematical analysis of the flow and allow for the use of potential flow theory.
| 2. What is the significance of inviscid flow in civil engineering? | |
Ans. Inviscid flow is significant in civil engineering as it allows engineers to analyze and predict the behavior of fluids in various structures and systems. By neglecting the effects of viscosity, engineers can simplify calculations and make design decisions based on the assumption of frictionless flow. This is particularly useful in designing fluid transport systems, such as pipelines and channels, where minimizing energy loss due to friction is important.
| 3. How does the assumption of incompressibility affect the analysis of fluid flow? | |
Ans. The assumption of incompressibility means that the fluid density remains constant throughout the flow. This assumption simplifies the mathematical equations used to analyze fluid flow by eliminating the need to consider changes in density. Incompressible flow is often used in civil engineering for practical purposes, as many fluids, such as water, can be approximated as incompressible under normal conditions.
| 4. What is the significance of irrotational flow in civil engineering applications? | |
Ans. Irrotational flow is significant in civil engineering as it allows for the analysis of fluid flow without considering the rotational motion of fluid particles. This simplifies the mathematical analysis and enables engineers to make design decisions based on potential flow theory. Irrotational flow is commonly used in the analysis of open channel flow, hydraulic structures, and aerodynamics.
| 5. What are the limitations of assuming inviscid, incompressible, irrotational flows? | |
Ans. The assumptions of inviscid, incompressible, irrotational flows have certain limitations. In reality, all fluids have some degree of viscosity, which affects the flow behavior. Additionally, compressibility effects become significant at high speeds or in the presence of large pressure gradients. Finally, the assumption of irrotational flow may not hold true in cases where vortices or rotational motion are important, such as in turbulent flow or near solid boundaries. Therefore, while these assumptions are useful for certain engineering analyses, they may not accurately represent real-world flow conditions in all cases.
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