3. Fluid Mechanics

Flow Kinematics — Quiz

Test your understanding of flow kinematics with 5 practice questions.

Practice Questions

Question 1

Which term in the acceleration expression $\vec{a}=\frac{D\vec{v}}{Dt}=\frac{\partial\vec{v}}{\partial t}+\vec{v}\cdot\nabla\vec{v}$ represents convective acceleration?

Question 2

For a one‐dimensional steady flow with velocity profile $u(x)=k\,x^{2}$, what is the acceleration $a_{x}$ of a fluid particle?

Question 3

In a two‐dimensional flow field given by $u=a\,x,\;v=b\,y$, what condition on constants $a$ and $b$ must hold for incompressible flow?

Question 4

What is the equation of the streamline passing through the point $(1,0)$ in the steady flow with velocity components $u=y$ and $v=-x$?

Question 5

A pipe with cross‐sectional area $A_{1}=0.10\;\mathrm{m^{2}}$ carries air of density $\rho_{1}=1.2\;\mathrm{kg/m^{3}}$ at velocity $v_{1}=3.0\;\mathrm{m/s}$. If downstream $\rho_{2}=0.6\;\mathrm{kg/m^{3}}$ and $A_{2}=0.05\;\mathrm{m^{2}}$, what is $v_{2}$?