Glycerine of density $1.25 \times 10^3 \, kg \, m^{-3}$ is flowing through a conical section of a pipe. The area of cross-section of the pipe at its ends is $10 \, cm^2$ and $5 \, cm^2$, and the pressure drop across its length is $3 \, N \, m^{-2}$. The rate of flow of glycerine through the pipe is $x \times 10^{-5} \, m^3 \, s^{-1}$. The value of $x$ is $..............$.

Water flows in a horizontal tube as shown in the figure. The pressure of water changes by $600\, N/m^2$ between $A$ and $B$ where the cross-sectional areas are $30\, cm^2$ and $15\, cm^2$ respectively. Find the rate of flow of water through the tube.

$A$ Venturimeter is used to:

When a fluid passes through a constricted part of a pipe, what happens to its velocity and pressure?

Consider a water tank as shown in the figure. Its cross-sectional area is $0.4\, m^{2}$. The tank has an opening $B$ near the bottom whose cross-sectional area is $1\, cm^{2}$. $A$ load of $24\, kg$ is applied on the water at the top. When the height of the water level is $40\, cm$ above the bottom,the velocity of water coming out of the opening $B$ is $v\, ms^{-1}$. The value of $v$,to the nearest integer,is ......$m/s$. [Take value of $g$ to be $10\, ms^{-2}$]

Air is streaming past a horizontal aeroplane wing such that its speed is $120\, m/s$ over the upper surface and $90\, m/s$ at the lower surface. If the density of air is $1.3\, kg/m^3$ and the wing is $10\, m$ long and has an average width of $2\, m$,then the difference of the pressure on the two sides of the wing is ........ $N/m^2$.