GATE2016-1-13

The instantaneous stream-wise velocity of a turbulent flow is given as follows:

$u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$

The time-average of the fluctuating velocity ${u}'(x,y,z,t)$ is

1. $\displaystyle{\frac{u'}{2}} \\$
2. $\displaystyle{\frac{-\overline{u}}{2}} \\$
3. $\text{zero}\\$
4. $\displaystyle{\frac{\overline{u}}{2}}$

recategorized

Related questions

A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kinematic viscosity,$v=30\times 10^{-6}$ $m^2/s$, the thermal boundary layer thickness (in $mm$) at $0.5 \:m$ from the leading edge is __________
Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity, $v_w=0.89\times 10^{-6}\:m^2/s$) is flowing through a model pipe of diameter $20 \:mm$. For satisfying the dynamic similarity, the velocity of water (in $m/s$) is __________
A channel of width $450$ $mm$ branches into two sub-channels having width $300$ $mm$ and $200$ $mm$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $0.9$ $m^3/s$ and the velocity in the ... , the velocity in the sub-channel of width $300$ $mm$ is _____________ $m/s$. Assume both inlet and outlet to be at the same elevation.
Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of $CO$ in the products is __________.