Deck 13: Measurements in Fluid Mechanics

Question 1

$\text {Air is flowing straight toward a building. What expression would provide \(\partial p / \partial x\) if \(x\)}$$\text { is measured perpendicular to the building? Neglect viscous and gravity effects and assume}$ $\text {steady flow.}$
(A) $\partial p / \partial x = - \rho ( u \partial u / \partial x - v \partial v / \partial y )$
(B) $\partial p / \partial x = - \rho u \partial u / \partial x$
(C) $\partial p / \partial x = - \rho v \partial u / \partial x$
(D) $\partial p / \partial x = - \rho ( u \partial u / \partial x - v \partial u / \partial y )$

Answer 1

B
$\partial p / \partial x = - \rho u \partial u / \partial x$
$\text {The \(x\)-component N-S equation (5.3.14), ignoring the viscous and gravity terms for a}$$\text { steady flow, is}$
$$\rho \frac { D u } { D t } = - \frac { \partial p } { \partial x } \quad \text { or } \quad \rho \left( u \frac { \partial u } { \partial x } + v \frac { \partial u } { \partial y } \right) = - \frac { \partial p } { \partial x }$$
$\text {Along the line that passes through the stagnation point, the \(y\)-component of the velocity }$$\text {\(v\) is zero. The pressure gradient is then}$
$$\frac { \partial p } { \partial x } = - \rho u \frac { \partial u } { \partial x }$$

Question 2

Euler's equation integrated along a streamline results in Bernoulli's equation providing 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

Answer 2

Constant density, steady, along a streamline, inviscid, in an inertial reference frame

Question 3

$$\text { If the stress component } \sigma _ { x x } \text { is given by } \sigma _ { x x } = - p + 2 \mu \partial u / \partial x \text {, the incompressible fluid is: }$$

A) Linear and isotropic
B) Isotropic and homogeneous
C) Linear and homogeneous
D) Linear, isotropic, and homogeneous

Answer 3

Linear and isotropic