A fluid of density \(\rho~\)is flowing in a pipe of varying cross-sectional area as shown in the figure. Bernoulli's equation for the motion becomes:

1. \(p+\dfrac12\rho v^2+\rho gh\text{ = constant}\)
2. \(p+\dfrac12\rho v^2\text{ = constant}\)
3. \(\dfrac12\rho v^2+\rho gh\text{ = constant}\)
4. \(p+\rho gh\text{ = constant}\)

A small hole of an area of cross-section \(2~\text{mm}^2\) is present near the bottom of a fully filled open tank of height \(2~\text{m}.\) Taking \((g = 10~\text{m/s}^2),\)${\mathrm{}}^{}$ the rate of flow of water through the open hole would be nearly:
1. \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\)
2. \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\)
3. \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\)
4. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)

A wind with a speed of \(40~\text{m/s}\) blows parallel to the roof of a house. The area of the roof is \(250~\text{m}^2.\) Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be:
\((\rho_{\text {air }}=1.2~\text{kg/m}^3)\)${\mathrm{ }}_{}$
1. \(4 \times 10^5~\text N,\) downwards
2. \(4 \times 10^5~\text N,\) upwards
3. \(2.4 \times 10^5~\text N,\) upwards
4. \(2.4 \times 10^5~\text N,\) downwards