Mechanics of Fluids 5th Edition By Potter - Test Bank

Mechanics of Fluids 5th Edition By Potter – Test Bank

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Mechanics of Fluids, 5th Edition Chapter 5: The Differential Forms of the
Fundamental Laws
14
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sections 5.1 and 5.2
1. Which of the following conditions is never a boundary condition in fluid mechanics?
(A) The velocity is zero at a boundary
(B) The normal component of velocity is zero in an inviscid flow at a boundary
(C) The tangential component of velocity is zero in an inviscid flow at a boundary
(D) The pressure is zero at a boundary
2. What four equations provide for the four unknowns u, v, w, p that are most often of interest in
fluid mechanics?
(A) Continuity, momentum
(B) Continuity, momentum, energy
(C) Continuity, momentum, energy, equation of state
(D) Continuity, momentum, energy, enthalpy relation
3. If the x-component of velocity u depends only on y in a plane incompressible flow, the
y-component of velocity v is:
(A) ( )f y
(B) const
(C) ( )f x
(D) 0
4. Three measurements are made of the x-component velocity in the diffuser of an
incompressible plane flow to be 32 m/s, 28 m/s and 20 m/s. The measurement points are
along the centerline of the symmetrical diffuser and are 4 cm apart. The y-component of the
velocity 2 cm above the centerline is approximated to be:
(A) 2 m/s
(B) 3 m/s
(C) 4 m/s
(D) 5 m/s

Mechanics of Fluids, 5th Edition Chapter 5: The Differential Forms of the
Fundamental Laws
15
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Section 5.3
1. If the stress component
σxx is given by 2 /xx p u x
σ
μ= − + ∂ ∂ , the incompressible fluid is:
(A) Linear and isotropic
(B) Isotropic and homogeneous
(C) Linear and homogeneous
(D) Linear, isotropic, and homogeneous
2. Euler’s equation integrated along a streamline results in Bernoulli’s equation provided the
flow is:
(A) Incompressible, inviscid, steady, in an inertial reference frame
(B) Constant density, steady, along a streamline, in an inertial reference frame
(C) Incompressible, steady, along a streamline, in an inertial reference frame
(D) Constant density, steady, along a streamline, inviscid, in an inertial reference frame
3. Air is flowing straight toward a building. What expression would provide ∂p/∂x if x is
measured perpendicular to the building? Neglect viscous and gravity effects and assume
steady flow.
(A) / ( / / )p x u u x v v y
ρ∂ ∂ = − ∂ ∂ − ∂ ∂
(B) / /p x u u x
ρ∂ ∂ = − ∂ ∂
(C) / /p x v u x
ρ∂ ∂ = − ∂ ∂
(D) / ( / / )p x u u x v u y
ρ∂ ∂ = − ∂ ∂ − ∂ ∂

Mechanics of Fluids, 5th Edition Chapter 5: The Differential Forms of the
Fundamental Laws
22
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Solutions for Sections 5.1 and 5.2
1. Which of the following conditions is never a boundary condition in fluid mechanics?
(C) The tangential component of velocity is zero in an inviscid flow at a boundary
The tangential component of velocity must be tangential to the boundary at a solid
boundary, but usually, if not always, in an inviscid flow it is nonzero. A porous
boundary would provide a normal component of velocity to the fluid at the
boundary.
The pressure is zero (gage) at a boundary if the boundary is a free surface, the
atmosphere.
In a viscous flow, the fluid sticks to the boundary so it takes on the velocity of
the boundary, which is usually zero.
2. What four equations provide for the four unknowns u, v, w, p that are most often of interest in
fluid mechanics?
(A) Continuity, momentum
The momentum equation is a vector equation containing the three velocity components
u, v, w, and p. Continuity provides the fourth equation. The energy differential equation
enters only when temperature is an unknown.
3. If the x-component of velocity u depends only on y in a plane flow, the y-component of
velocity v is:
(C) ( )f x
The differential continuity equation / / 0u x v y∂ ∂ + ∂ ∂ = is used:
0 ( ) and ( ).
u v v f y v f x
x y
∂ ∂
= = − ∴ ≠ =
∂ ∂
It could be a constant, or 0, but not necessarily so. It is not a function of y.
Mechanics of Fluids, 5th Edition Chapter 5: The Differential Forms of the
Fundamental Laws
23
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4. Three measurements are made of the x-component velocity in the diffuser of an
incompressible plane flow to be 32 m/s, 28 m/s and 20 m/s. The measurement points are
along the centerline of the symmetrical diffuser and are 4 cm apart. The y-component of the
velocity 2 cm above the centerline is approximated to be:
(B) 3 m/s
We chose to use the more accurate central difference to approximate the derivative
since the information given allows such an approximation:
20 32 m/s
150
0 08 m
u u
x x
∂ ∆ −
≅ = = −
∂ ∆ .
The continuity equation then provides
2
2
0
150 or 150 3 m/s
0 02 .
.
vv u v v v
y x y y
−∂ ∂ ∂ ∆
= − = ≅ = = ∴ =
∂ ∂ ∂ ∆

Mechanics of Fluids, 5th Edition Chapter 5: The Differential Forms of the
Fundamental Laws
24
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Solutions for Section 5.3
1. If the stress component
σxx is given by 2 /xx p u x
σ
μ= − + ∂ ∂ , the incompressible fluid is:
(A) Linear and isotropic
The fluid is homogeneous if fluid properties, such as
μ, do not depend on position. That
leaves only (A) as a possibility. The fluid must be linear, that is, there must be a linear
relation between the velocity and the stress components. It must also be isotropic, i.e., it
must have the same properties in all directions at a given point in the flow.
2. Euler’s equation integrated along a streamline results in Bernoulli’s equation provided the
flow is:
(D) Constant density, steady, along a streamline, inviscid, in an inertial reference frame
Remember, constant density is more restrictive than incompressible. To move the
density
ρ outside the integral symbol requires that
ρ = const.
3. Air is flowing straight toward a building. What expression would provide ∂p/∂x if x is
measured perpendicular to the building? Neglect viscous and gravity effects and assume
steady flow.
(B) / /p x u u x
ρ∂ ∂ = − ∂ ∂
The x-component N-S equation (5.3.14), ignoring the viscous and gravity terms for a
steady flow, is
or
p pDu u u
u v
Dt x x y x
ρ
ρ  ∂ ∂∂ ∂
= − + = − 
∂ ∂ ∂ ∂ 
Along the line that passes through the stagnation point, the y-component of the velocity
v is zero. The pressure gradient is then
p u
u
x x
ρ
∂ ∂
= −
∂ ∂