Respuesta :
Answer:
The gauge pressure is 1511.11 psi.
Explanation:
Given that,
Flow rate = 94 ft³/min
Diameter d₁=3.3 inch
Diameter d₂ = 5.2 inch
Pressure P₁= 15 psi
We need to calculate the pressure on other side
Using Bernoulli equation
[tex]P_{1}+\dfrac{1}{2}\rho v_{1}^2=P_{2}+\dfrac{1}{2}\rho v_{2}^2[/tex]
We know that,
[tex]V=Av[/tex]
[tex]v=\dfrac{V}{A}[/tex]
Where, V = volume
v = velocity
A = area
Put the value of v into the formula
[tex]P_{1}+\dfrac{1}{2}\rho (\dfrac{V}{A_{1}})^2=P_{2}+\dfrac{1}{2}\rho (\dfrac{V}{A_{2}})^2[/tex]
Put the value into the formula
[tex]15+\dfrac{1}{2}\times0.36\times(\dfrac{2707.2\times4}{\pi\times(3.3)^2})^2=P_{2}+\dfrac{1}{2}\times0.36\times(\dfrac{2707.2\times4}{\pi\times(5.2)^2})^2[/tex]
[tex]P_{2}=15+\dfrac{1}{2}\times0.036\times(\dfrac{2707.2\times4}{\pi\times(3.3)^2})^2-\dfrac{1}{2}\times0.036\times(\dfrac{2707.2\times4}{\pi\times(5.2)^2})^2[/tex]
[tex]P_{2}=1525.8\ psi[/tex]
We need to calculate the gauge pressure
Using formula of gauge pressure
[tex]P_{g}=P_{ab}-P_{atm}[/tex]
Put the value into the formula
[tex]P_{g}=1525.8-14.69[/tex]
[tex]P_{g}=1511.11\ psi[/tex]
Hence, The gauge pressure is 1511.11 psi.
