Question

(20.1) A very large tank of water with its top open to the air has a small hole in its side. The hole lies at a depth of 9.8m below the top surface of the water. Compute the speed with which water spurts out of the hole. [Take g = 10m/s2 and assume that the hole is small enough that the water level in the tank is changing very slowly.]

(20.2) Modern construction standards require that roofs be securely attached to the walls of buildings. Consider a particular flat roof, comprised of panels with length L = 12 m and width W = 5m, which are not held down by any additional means other than their own weight. It was observed – for a particular flat roof – that a sustained wind of 180km/h blowing across it was sufficient to cause the panel to lift off of the walls which were supporting it. Estimate the weight of this roof panel. [Take g = 10m/s2 and the density of air to be ρair = 1.2kg/m3. Also, assume that the thickness of the roof panel is insignificant.]

Answer 1

Question (20.1) is the toricelli's special condition obtained from the general equation of Bernoulli's equation. At the end, the equation just follows the free fall equation.

Question (20.2) also follows the Bernoulli's equation as shown in the below two images. The area of the rooftop is calculated. Conditions from the question are applied to the bernoulli's equation and the pressure variation between bottom and top of the rooftop just when it's been lift is found.

Using the obtained pressure we find the force curresponding to it. From that we obtain the Mass as well as Weight on Earth as shown in the below image.