A and B are the end -points of a diameter of a disc rolling along a straight line with a counter Clock-wise angular velocity as shown in the figure. Referring to the velocity vectors $${\overline V _A}$$ and $${\overline V _B}$$ shown in the figure:

A jet of water with a velocity $${V_1}$$ (Figure shown below) and area of cross-section $${A_1}$$ enters a stream of slow moving water in a pipe of area $${A_2}$$ and velocity $${V_2}$$. The two streams enter with the same pressure $${P_1}$$. After thoroughly mixing in the pipe the stream emerges as a single stream with velocity $${V_3}$$ and pressure $${p_2}$$. If there are no losses in the flow, determine $$\left( {{p_2} - {p_1}} \right)$$ for
$${V_1} = 20\,\,m/s,\,\,$$
$${V_2} = 10\,\,m/s,\,\,$$
$${A_1} = 0.01\,\,{m^2},\,$$
$$\,{A_2} = 0.02\,{m^2},$$
density of water $$\rho = 1000kg/{m^3}.$$

The predominant forces acting on an element of fluid in the boundary layer over a flat plate in a uniform parallel stream are:

The cross-sectional area of one limb of a U-tube manometer [ Figure shown below ] is made $$500$$ time larger than the other, so that the pressure difference between the two limbs can be determined by measuring $$'h'$$ on one limb of the manometer. The percentage error involved is :