Consider the following equation of Bernoulli's theorem: $P + \frac{1}{2}\rho V^2 + \rho gh = K$ (constant). The dimensions of $K/P$ are the same as those of which of the following?

$A$ manometer connected to a closed tap reads $3.5 \times 10^5 \ N/m^2$. When the valve is opened,the reading of the manometer falls to $3.0 \times 10^5 \ N/m^2$. The velocity of the flow of water is ........ $m/s$.

Different heads are in Column - $I$ and their formulas are given in Column - $II$. Match them appropriately.

Column - $I$	Column - $II$
$(a)$ Velocity head	$(i)$ $\frac{P}{\rho g}$
$(b)$ Pressure head	$(ii)$ $h$
$(c)$ Potential head	$(iii)$ $\frac{v^2}{2g}$

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 $..............$.

Explain blood flow and heart attack with the help of Bernoulli's principle.

An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$