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.  \(p+\frac12\rho v^2+\rho gh\text{=constant}\)
2. \(p+\frac12\rho v^2\text{=constant}\)
3. \(\frac12\rho v^2+\rho gh\text{=constant}\)
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 \(40\) m/s blows parallel to the roof of a house. The area of the roof is \(250\) m². 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: (\(\rho_{\text {air }}=1.2\)${\mathrm{ }}_{}\mathrm{kg}/{\mathrm{m}}^3$)
1. \(4 \times 10^5\) N, downwards
2. \(4 \times 10^5\) N, upwards
3. \(2.4 \times 10^5\) N, upwards
4. \(2.4 \times 10^5\) N, downwards