Answer:
The value is [tex]P_1 = 314645 \ Pa [/tex]
Explanation:
From the question we are told that
The height is [tex]h_2 = 10 m[/tex]
The height of the burning roof is [tex]k = 9 m[/tex]
The horizontal distance is [tex]d = 7 \ m[/tex]
The height of the truck is [tex]h_1 = 0.5 \ m[/tex]
Generally the time for the water to hit the roof from the hose is mathematically represented as
[tex]t = \sqrt{\frac{2 * (h_2 - k)}{g} }[/tex]
=> [tex]t = \sqrt{\frac{2 * (10 - 9)}{9.8} }[/tex]
=> [tex]t = 0.4518 \ s [/tex]
Generally the velocity of the water is mathematically evaluated as
[tex]v_2 = \frac{d}{t}[/tex]
[tex]v_2 = \frac{ 7}{0.4518}[/tex]
[tex]v_2 = 15.5 \ m/s [/tex]
Generally from Bernoulli's Equation we have that
[tex]P_1 + \frac{1}{2} v_1^2 * \rho + \rho *g *h_1 = P_2 + \frac{1}{2} v_2^2 * \rho + \rho *g *h_2[/tex]
Here [tex]P_1 [\tex] is pressure in the chamber which we are to calculate , [tex]P_2 [\tex] is the atmospheric pressure with value [tex]P_2 = 101325 \ Pa [\tex] , [tex]v_1 [\tex] is the velocity of the water before it starts flowing with value [tex]v_1 = 0 m/s [\tex] , [tex]\rho [\tex] is the density of water with value [tex]\rho = 1000 \ kg/m^3 [\tex]
So
[tex]P_1 + \frac{1}{2} 0^2 * 1000 + 1000 *9.81 *0.5 = 101325 + \frac{1}{2}* 15.5^2* 1000 + 1000 *9.81 *10[/tex]
[tex]P_1 = 314645 \ Pa [/tex]
