Finite Element Method Questions and Answers – Potential Flow, Seepage, Electric & Magnetic Fields and Fluid Flow Ducts

This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Potential Flow, Seepage, Electric & Magnetic Fields and Fluid Flow Ducts”.

1. How to find out the velocities of flow from the stream function?
a) Take Partial derivatives
b) Take total derivatives
c) Partial Integration
d) Total integration

Explanation: Once the stream function is known, the velocity components can be found out by partially differentiating the same. It is mathematically represented as
u = dΨ / dy
v = – dΨ / dx
where Ψ = stream function
u, v = velocity components along x and y directions respectively.

2. What is the governing equation of a potential flow problem?
a) d2Ψ / dx2 – d2Ψ / dy2 = 0
b) d2Ψ / dx2 + d2Ψ / dy2 = 0
c) d2Ψ / dx2 * d2Ψ / dy2 = 0
d) d2Ψ / dx2 / d2Ψ / dy2 = 0

Explanation: The governing equation of a potential flow problem is given by d2Ψ / dx2 + d2Ψ / dy2 = 0. This helps determine the unknown values of flow velocities. Ψ is the stream function in the z direction. The value of stream function remains constant along a stream line.

3. “Flow of water occurring in land drainage or seepage under dams can be described by a Laplace equation.” What is the general form of the equation under discussion?
a) d / dx(kxdΦ / dx) + d / dy(kydΦ / dy) = 1
b) d / dx(kxdΦ / dx) – d / dy(kydΦ / dy) = 0
c) d / dx(kxdΦ / dx) + d / dy(kydΦ / dy) = 0
d) d / dx(kxdΦ / dx) + d / dy(kydΦ / dy) = 4

Explanation: Flow of water occurring in land drainage or seepage under dams can be described by the Laplace equation – d / dx(kxdΦ / dx) + d / dy(kydΦ / dy) = 0.
kx and ky = hydraulic conductivities in the x and y direction.

4. Which law helps us to determine the fluid velocity components in seepage problems?
a) Rayleigh Law
b) Euler Law
c) Reynolds Law
d) Darcy Law

Explanation: In seepage and flow of water in land drainage problems, the fluid velocity components can be found out using the Darcy Law. This law is based on the principle of movement of fluid over a given substance. It states that, flow between any two points is directly proportional to the pressure differences, distance and connectivity of points under consideration.

5. Which equation governs the pressure drop occurring in flow of a fluid in long pipes?
a) Δp = 2fρv2mL / Dh
b) Δp = 4fρv2mL / Dh
c) Δp = 3fρv2mL / Dh
d) Δp = ρv2mL / Dh

Explanation: The expression for pressure drop occurring in fluid flow of long pipes is given by Δp = 2fρv2mL / Dh.
where f = friction factor
ρ = density
vm = mean velocity of fluid
L = Length of duct
Dh = Hydraulic diameter
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