Dimensional Analysis

 Question 1
The dimension of dynamic viscosity is:
 A $ML^{-1}T^{-1}$ B $ML^{-1}T^{-2}$ C $ML^{-2}T^{-2}$ D $ML^{0}T^{-1}$
GATE CE 2022 SET-2   Fluid Mechanics and Hydraulics
Question 1 Explanation:
Unit of dynamic viscosity $=\frac{kg}{m.s} \; or \; \frac{Ns}{m^2}=ML^{-1}T^{-1}$
 Question 2
Kinematic viscosity' is dimensionally represented as
 A $\frac{M}{LT}$ B $\frac{M}{L^{2} T}$ C $\frac{T^{2}}{L}$ D $\frac{L^{2}}{T}$
GATE CE 2021 SET-1   Fluid Mechanics and Hydraulics
Question 2 Explanation:
Kinematic viscosity
$v=\frac{\mu }{\rho }=\frac{kg/m\cdot s}{kg/m^3}=m^2/s$
$[v]=\frac{m^2}{s }=\frac{L^2}{T}$

 Question 3
In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are 0.05 $m^{3}$/s and 0.25 m/s, respectively. If the full scale structure (30 times bigger) is subjected to a discharge of 270 $m^{3}$/s, then the time scale (model to full scale) value (up to two decimal places) is ______
 A 0 B 0.18 C 0.55 D 0.75
GATE CE 2018 SET-1   Fluid Mechanics and Hydraulics
Question 3 Explanation:
\begin{aligned} \text { Froude Law }(F r)_{m}&=(F r)_{p} \\ \left(\frac{V}{\sqrt{L \mathrm{g}}}\right)_{m} &=\left(\frac{v}{\sqrt{L g}}\right)_{p} \quad\left(g_{m}=g_{p}\right) \\ v_{r} &=\sqrt{L_{r}} \\ \text{or}\quad \frac{L_{r}}{T_{r}} &=\sqrt{L} \\ T_{r} &=\sqrt{L_{r}} \\ T_{r} &=\sqrt{\frac{1}{30}}=0.1826 \end{aligned}
 Question 4
A 1:50 model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is 1000 $m^{3}/s$. The corresponding discharge (in $m^{3}/s$, up to two decimal places) to be maintained in the model, neglecting variation in acceleration due to gravity, is ______
 A 0.01 B 0.06 C 0.5 D 0.1
GATE CE 2018 SET-1   Fluid Mechanics and Hydraulics
Question 4 Explanation:
Froude law is valid
\begin{aligned} Q_{r} &=L_{r}^{25} \\ \frac{Q_{m}}{Q_{p}} &=\left(\frac{1}{50}\right)^{25} \\ \frac{Q_{m}}{1000} &=\left(\frac{1}{50}\right)^{25} \\ Q_{m} &=0.0566 \mathrm{m}^{3 / \mathrm{s}} \\ \text{So},\quad Q_{m} & \simeq 0.06 \mathrm{m}^{3 / \mathrm{s}} \end{aligned}
 Question 5
The relationship between the length scale ratio $(L_{r})$ and the velocity scale ratio $(V_{r})$ in hydraulic models, in which Froude dynamic similarity is maintained, is:
 A $V_{r}=L_{r}$ B $L_{r}=\sqrt{V_{r}}$ C $V_{r}=L_{r}^{1.5}$ D $V_{r}=\sqrt{L_{r}}$
GATE CE 2015 SET-2   Fluid Mechanics and Hydraulics
Question 5 Explanation:
As per Froude Law
\begin{aligned} \left(\frac{V}{\sqrt{L g}}\right)_{m}&=\left(\frac{V}{\sqrt{L g}}\right)_{p} \\ \Rightarrow \quad V_{r}&=\sqrt{L_{r}} \end{aligned}

There are 5 questions to complete.