Answer:
The velocity is [tex]v_n =14.09 \ m/s[/tex]
Explanation:
From the question we are told that
The velocity of the water in the pipe is [tex]v_i = 1.0 \ m/s[/tex]
The pressure inside the pipe is [tex]P_i = 200000 \ Pa[/tex]
The pressure at the nozzle is [tex]P_n = 101300 \ Pa[/tex]
The density of water is [tex]\rho = 1000 \ kg / m^3[/tex]
For the height [tex]h_1 = h_2 = h[/tex]
where [tex]h_1[/tex] is height of water in the pipe
and [tex]h_2[/tex] is height of water at the nozzle
Generally Bernoulli equation is represented as
[tex]\frac{1}{2} \rho * v_i ^2 + \rho * g * h_1 + P_i = \frac{1}{2} \rho v_n ^2 + \rho * g* h_2 + P_n[/tex]
=> [tex]\frac{1}{2} \rho * v_i ^2 + \rho * g * h + P_1 = \frac{1}{2} \rho v_n ^2 + \rho * g* h + P_2[/tex]
Where [tex]v_n[/tex] is the velocity of the water at the nozzle
Now making [tex]v_n[/tex] the subject
[tex]v_n = \sqrt{\frac{2}{\rho} [ P_i - Pn + \frac{1}{2} \rho v_i^2}[/tex]
substituting values
[tex]v_n = \sqrt{\frac{2}{1000} [ 200000 - 101300 + \frac{1}{2} (1000 * (1.0)^2)}[/tex]
[tex]v_n =14.09 \ m/s[/tex]
The velocity of the water exiting the nozzle is equal to 14.09 m/s.
Given the following data:
To calculate the velocity of the water exiting the nozzle, we would apply Bernoulli's equation:
Note: There's no change in height.
Mathematically, the velocity of the water exiting the nozzle is given by this formula:
[tex]V_n =\sqrt{\frac{2}{\rho} (P_i - P_n + \frac{1}{2} \rho v^2)}[/tex]
Substituting the given parameters into the formula, we have;
[tex]V_n =\sqrt{\frac{2}{1000} (200000 - 101300 + \frac{1}{2} \times 1000 \times 1^2)}\\\\V_n =\sqrt{\frac{1}{500} (98700 + 500)}\\\\V_n =\sqrt{\frac{1}{500} (99200)}\\\\V_n =\sqrt{198.4}[/tex]
Exit velocity = 14.09 m/s
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