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BIEN 501 Physiological Modeling
Makeup Exam
April 21, 2004
Circle the most correct answer to each question. An answer is considered to be “correct” if it is
within 1% of the correct answer.
1) Newton's law of viscosity
According to Newton's law of viscosity, the shear stress in a fluid is
(a) inversely proportional to the depth of the fluid
(b) proportional to the depth of the fluid
(c) inversely proportional to the velocity gradient in the fluid
(d) proportional to the velocity gradient in the fluid
(e) none of the above
--------------------------------------------------------------------------------------------------------------------2) Viscosity
What is the primary difference between dynamic viscosity (µ) and kinematic viscosity
(ν)?
(a) Kinematic viscosity is independent of pressure.
(b) Dynamic viscosity is independent of pressure.
(c) Dynamic viscosity is independent of temperature.
(d) Kinematic viscosity is independent of temperature.
(e) none of the above
--------------------------------------------------------------------------------------------------------------------3) A Newtonian fluid
(a) is a fluid in which shear stress is proportional to the velocity gradient, perpendicular
to the plane of shear. The constant of proportionality is known as the viscosity.
(b) is a fluid in which shear stress is proportional to the velocity gradient, parallel to the
plane of shear. The constant of proportionality is known as the viscosity.
(c) is a fluid in which shear stress is not simply proportional solely to the velocity
gradient, perpendicular to the plane of shear.
(d) is a fluid in which shear stress is not simply proportional solely to the velocity
gradient, parallel to the plane of shear.
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------4) Equation of Continuity
The continuity equation is another name for the
(a) conservation of linear momentum.
1
Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
(b) conservation of energy.
(c) conservation of mass equation.
(d) conservation of angular momentum.
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------5) Euler equation
Euler equations neglect the effect
(a ) of the viscosity of the fluid which are also absent in the Navier-Stokes equations.
(b) of the viscosity of the fluid which are included in the Navier-Stokes equations.
(c) density of the fluid.
(d) b & c
(e) none of the above
--------------------------------------------------------------------------------------------------------------------6) Buoyancy
Which one of the following statements concerning the buoyant force on an object
submerged in a liquid is true?
(a) The buoyant force depends on the mass of the object.
(b) The buoyant force depends on the weight of the object.
(c) The buoyant force is independent of the density of the liquid.
(d) The buoyant force depends on the volume of the liquid displaced.
(e) none of the above
--------------------------------------------------------------------------------------------------------------------7) Poiseuille flow
Description of Poiseuille flow
(a) Flow profile is non- linear.
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Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
(b) Laminar, incompressible, viscous flow due to only shear. Flow profile is linear.
(c) Laminar, compressible.
(d) Laminar, incompressible, viscous flow due to only pressure gradient. Flow profile is
parabolic.
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------8) Shear Stress
Physical meaning of fluid stress components σxy and σxx ?
(a) σxy is the shear stress acting on the surface element perpendicular to the x-axis. σxy
is parallel to the surface and points to the y direction .σxx is the normal stress pointing to
the x direction and acting on the surface element perpendicular to the x- axis.
(b) σxy is the shear stress acting along the surface element parallel to the x-axis. σxy is
perpendicular to the surface and points to the y direction . σxx is the normal stress
pointing to the x direction and acting on the surface element perpendicular to the x- axis.
(c) σxy is the shear stress acting on the surface element perpendicular to the x-axis. σxy
is parallel to the surface and points to the y direction . σ xx is the normal stress pointing to
the x direction and acting on the surface element parallel to the x- axis.
(d) σxy is the shear stress acting on the surface element perpendicular to the x-axis. σxy
is parallel to the surface and points to the y direction . σ xx is the normal stress pointing to
the y direction and acting on the surface element perpendicular to the x- axis.
(e) none of the above
--------------------------------------------------------------------------------------------------------------------9) Navier-stokes equation
The main terms in the Navier-stokes equation
represents
(a) material derivative of velocity times the density which represents the unsteady and
convective acceleration of fluid particle per unit volume on one side and contains sum of
forces per unit volume including gravitational forces , pressure forces and viscous
forces.
3
Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
(b) material derivative of velocity times the density which represents the unsteady and
convective acceleration of fluid particle per unit volume on one side and contains sum of
forces per unit volume including gravitational forces and pressure forces.
(c) material derivative of velocity times the density which represents the steady and
convective acceleration of fluid particle per unit volume on one side and contains sum of
forces per unit volume including gravitational forces , pressure forces and viscous
forces.
(d) material derivative of velocity times the density which represents the steady and
convective acceleration of fluid particle per unit volume on one side and contains sum of
forces per unit volume including gravitational forces and viscous forces.
(e) none of the above
--------------------------------------------------------------------------------------------------------------------10) Stream function
If a flow field can be described by a stream function, ψ, what can you say about the
flow?
(a) flow is 3 dimensional.
(b) it is equivalent to saying that the flow is compressible.
(c) it is equivalent to saying that the flow is incompressible.
(d) flow may be 2 D or 3 D.
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------11) Viscosity
Viscosity of the fluid can be obtained from terminal velocity of a sphere in the fluid using
(a) Buoyant force only.
(b) Buoyant and Kinetic force.
(c) Stokes Law
(d) Force of gravity on the sphere in the direction of fall, buoyant force and kinetic forces.
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------12) Equation of change
When potential energy Φ is introduced in the equation of change for kinetic energy,
(- ρ(V.
Φ)) can be rewritten as
(a) -( . ρV Φ) + Φ(
(b) d (1/2 ρV2 + ρ Φ)
(c) Φ
(d) a and c only
.ρV)
4
Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
(e) none of the above.
--------------------------------------------------------------------------------------------------------------------13) Cone and plate viscometer
In a cone and plate viscometer, which of the boundary conditions are used
(a) μ (r, φ) = 0 at φ= π/ 2 only
(b) μ(r, φ) = ωR at φ= π/ 2 + θ only
(c) μ(r, φ) = ωR at φ= π/ 2 - θ only
(d) a & c
(e) none of the above
--------------------------------------------------------------------------------------------------------------------14) Biomedical Application
For someone at rest, the average flow rate out of the aorta of the heart is 90 mls -1. It is
because of which of the following principles this flow rate is the same as through the
connected arterioles, capillaries and veins.
(a) Poiueselle flow
(b) continuity principle
(c) Womersley flow
(d) conservation of energy
(e) none of the above
--------------------------------------------------------------------------------------------------------------------15) Differential equation
A differential equation is linear if
(a) it is linear in the dependent variable
(b) it has the property of putting the dependent variable(s) to zero
(c) it has only one independent variable.
(d) it has more than one independent variables.
(e) none of the above
--------------------------------------------------------------------------------------------------------------------16) The velocity distribution of a viscous liquid (dynamic viscosity μ = 0.9 Ns/m2) flowing
over a fixed plate is given by u = 0.68y - y2 (u is velocity in m/s and y is the distance from
the plate in m). What are the shear stresses at the plate surface and at y=0.34m?
(a) 0.78
(b) 2.1
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Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
(c) 1.0
(d) zero
(e) none of the above
--------------------------------------------------------------------------------------------------------------------17) In a fluid the velocity measured at a distance of 75mm from the boundary is
1.125m/s. The fluid has absolute viscosity 0.048 Pa s and relative density 0.913. What is
the velocity gradient and shear stress at the boundary assuming a linear velocity
distribution.
(a) 0.702 Pas
(b) 0.54 Pas
(c) 2.9 Pas
(d) 0.671 Pas
(e) None of the above
--------------------------------------------------------------------------------------------------------------------18) Dimension Analysis
Dimensions of Viscosity are
(a) MT-2
(b) M L-1T-1
(c) ML-1T-2
(d) No dimension
(e) None of the above
--------------------------------------------------------------------------------------------------------------------19) Boundary layer theory
For two-dimensional steady laminar flow over a flat plate, the boundary layer equations
are given below.
Continuity
x-momentum
6
Shweta S Khedlekar
Makeup Exam
BIEN 501 Physiological Modeling
April 21, 2004
Here, u and v are the components of the velocity vector in the x and y directions, and v
is the kinematic viscosity. The appropriate boundary conditions on u(x, y ) and v(x, y) .
(a) No slip at rigid the rigid surface:
u(x, 0 )= 0
(b) No flow normal to the rigid surface (kinematic condition):
v(x, 0)=0
(c) Free stream velocity is approached far from the plate:
u (x, y→∞)→U∞
(d)All of the above
(e)None of the above.
--------------------------------------------------------------------------------------------------------------------20) Vectors
Differential operations involving the
[
x V] r is equal to
- operator in cylindrical co-ordinates (r, θ, z),
(a) 1/r (d Vz/d θ ) – (d Vθ/d z)
(b) (d Vr/d z ) – (d Vz/d r)
(c) 1/r (d (r Vθ)/d r ) – 1/r(d Vr/d θ )
(d) (d V θ /d z ) – (d Vz/d r)
(e) None of the above
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