Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $$20$$ $$mm$$ with uniform velocity of $$2$$ $$m/s.$$ Acceleration due to gravity is $$9.81$$ $$m/{s^2}.$$ Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter in mm of the stream $$0.5$$ $$m$$ below the tap is approximately

For steady, fully developed flow inside a straight pipe of diameter $$D,$$ neglecting gravity effects, the pressure drop $$\Delta p$$ over a length $$L$$ and the wall shear stress $${\tau _w}$$ are related by

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by $$k = {k_0} + bT;$$ where $${k_0}$$ and $$b$$ are positive constants, and $$T$$ is temperature.

As $$x$$ increases, the state temperature gradient $$(dT/dx)$$ will

Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \le x \le L} \right),$$ through a planewall with the boundary surfaces $$(x=0$$ and $$x=L)$$ maintained at temperatures of $${0^ \circ }C$$ and $${100^ \circ }C$$. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.