Answer:
The velocity in duct is 73.854 m/s.
Explanation:
Given that Pitot tube measuring velocity v in 50 cm diameter duct contain air of density 1.1 [tex]\frac{kg}{m^{3} }[/tex].
Also, P1 = Pressure in duct is 97kpa and P2 = Pressure at impact or stagnation point is 100kpa.
Using Bernoulli equation,
[tex]P+\frac{1}{2}\rho v^{2} +\rho gh=0[/tex]
When air is flowing through duct,
[tex]97,000+\frac{1}{2}\rho v^{2} +\rho gh1=0[/tex]
When air is at stagnation point.
[tex]1,00,000+0+\rho gh1=0[/tex]
Comparing both the equation,
[tex]97,000+\frac{1}{2}\rho v^{2} +\rho gh1=1,00,000+\rho gh1[/tex]
[tex]\frac{1}{2}\rho v^{2}=3000[/tex]
[tex] 0.55v^{2}=3000[/tex]
[tex] v^{2}=5454.54[/tex]
v=73.854 m/s.
Therefore, The velocity in duct is 73.854 m/s.
