The wind blows at a speed of 100 km/hr in a storm. Calculate the force acting on a 1 m x 2 m window which is facing the storm. The window is in a high-rise building. The wind speed is not affected by ground effects. Assume density of air as 1.2 kg/m^3

Question

The wind blows at a speed of [latex]100 {km}/{hr}[/latex] in a storm. Calculate the force acting on a [latex] 1 m imes 2 m[/latex] window which is facing the storm. The window is in a high-rise building. The wind speed is not affected by ground effects. Assume density of air as [latex]1.2 {kg}/{m^{3}}[/latex]

Accepted Answer

The pressure on the window facing the storm will be stagnation pressure as velocity of the wind is zero. Working with gauge pressures, the pressure upstream in the wind is zero.

Velocity of the wind = [latex]\frac{100 imes 1000}{3600} = 27.8 {m}/{s}[/latex]

Applying Bernoullis equation to calculate the pressure on the window

[latex] \frac{P_{1}}{\gamma } + \frac{V^{2}_{1}}{2g} + z_{1} = \frac{P_{2}}{\gamma } + \frac{V^{2}_{2}}{2g} + z_{2}[/latex]

where we have [latex]z_{1} = z_{2} ; P_{1} = 0; V_{2} = 0, and P_{2} = P_{0} [/latex]

[latex] herefore \frac{P_{0}}{\gamma } = \frac{V^{2}_{1}}{2g}; P_{0} = \frac{ ho V^{2}_{1}}{2}[/latex]

Substituing proper values

[latex] P_{0} = \frac{1.2 imes \left(27.8 ight)^{2} }{2} = 464 {N}/{m^{2}}[/latex]

Force = [latex]P_{0} \cdot A = 464 imes 1 imes 2[/latex]

F = 928 N

Question 2.8: The wind blows at a speed of 100 km/hr in a storm. Calculate...

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