Moderate -0.5 This is a straightforward dimensional analysis problem requiring students to rearrange the given formula and substitute known dimensions. While it requires understanding that R is dimensionless and knowing standard dimensions (density, velocity, length), it's a mechanical application of dimensional analysis with no conceptual subtlety or multi-step reasoning—easier than average but not trivial.
The Reynolds number, \(R\), is an important dimensionless quantity in fluid dynamics; it can be used to predict flow patterns when a fluid is in motion relative to a surface.
The Reynolds number is defined as $$R = \frac{\rho ul}{\mu},$$
where \(\rho\) is the density of the fluid, \(u\) is the velocity of the fluid relative to the surface, \(l\) is the distance travelled by the fluid and \(\mu\) is the viscosity of the fluid.
Find the dimensions of \(\mu\). [4]
Question 2:
2 | ML 3
uLT 1
ul ML3 LT1 L
ML 1T 1 | B1
B1
M1
A1
[4] | 1.2
1.2
1.1
1.1 |
Rearrange correctly to make the
subject and use the fact that R is
dimensionless and substitute their
and u
1s 1
SC: B2 for kg m | Condone lower case
The Reynolds number, $R$, is an important dimensionless quantity in fluid dynamics; it can be used to predict flow patterns when a fluid is in motion relative to a surface.
The Reynolds number is defined as $$R = \frac{\rho ul}{\mu},$$
where $\rho$ is the density of the fluid, $u$ is the velocity of the fluid relative to the surface, $l$ is the distance travelled by the fluid and $\mu$ is the viscosity of the fluid.
Find the dimensions of $\mu$. [4]
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2019 Q2 [4]}}