# GATE2016-1-40

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 __________

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## 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 __________
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 $\displaystyle{\frac{u'}{2}} \\$ $\displaystyle{\frac{-\overline{u}}{2}} \\$ $\text{zero}\\$ $\displaystyle{\frac{\overline{u}}{2}}$
The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary bottom plate at a speed of $3\: m/s$. The flow between the plates is solely due to the motion of the top plate. The force per ... _________ $N/m^2$. Viscosity of the fluid $μ = 0.44 \:kg/m-s$ and density $\rho = 888 \: kg/m^3$.