Answer:
The pressure difference is [tex]\Delta P = 1.46 *10^{5}\ Pa[/tex]
Explanation:
From the question we are told that
The density is [tex]\rho = 1250 \ kg/m^3[/tex]
The speed at location 1 is [tex]v_1 = 9.93 \ m/s[/tex]
The diameter at location 1 is [tex]d_1 = 11.1\ cm = 0.111 \ m[/tex]
The diameter at location 2 is [tex]d_1 = 16.7\ cm = 0.167 \ m[/tex]
The height at location 1 is [tex]h_1 = 8.89 \ m[/tex]
The height at location 2 is [tex]h_2 = 1 \ m[/tex]
Generally the cross- sectional area at location 1 is mathematically represented as
[tex]A_1 = \pi * \frac{d^2}{4}[/tex]
=> [tex]A_1 = 3.142 * \frac{ 0.111^2}{4}[/tex]
=> [tex]A_1 = 0.0097 \ m^2[/tex]
Generally the cross- sectional area at location 2 is mathematically represented as
[tex]A_2 = \pi * \frac{d_1^2}{4}[/tex]
=> [tex]A_2= 3.142 * \frac{ 0.167^2}{4}[/tex]
=> [tex]A_2 =0.0219 \ m^2[/tex]
From continuity formula
[tex]v_1 * A_1 = v_2 * A_2[/tex]
=> [tex]v_2 = \frac{A_1 * v_1}{A_2 }[/tex]
=> [tex]v_2 = \frac{0.0097 * 9.93}{0.0219 }[/tex]
=> [tex]v_2 = 4.398 \ m/s[/tex]
Generally according to Bernoulli's theorem
[tex]P_1 + \rho * g * h_1 + \frac{1}{2} \rho * v_1^2 = P_2 + \rho * g * h_2 + \frac{1}{2} \rho * v_2^2[/tex]
=> [tex]P_2 - P_1 = \frac{1}{2} \rho (v_1 ^2 - v_2^2 ) + \rho* g (h_1 - h_2)[/tex]
=> [tex]\Delta P = \frac{1}{2}* 1250* (9.93 ^2 - 4.398^2 ) + 1250* 9.8 (8.89- 1)[/tex]
=> [tex]\Delta P = 1.46 *10^{5}\ Pa[/tex]
