Respuesta :
ρgh is the gravitational component of Bernoulli's equation
the pipe is horizontal
so no change in h
ρgh is equal on both sides
cancels out
now
v (velocity) is inversely proportional to square of radius
so
v_2 / v_1 = (r_1 )^2 / (r_2)^2 = 1.1^2 / 0.66^2 = 2.78
v_2 = 2.78 v_2
and
8130 N/m² + ((821 kg/m³) * (v_1)²)/2 = 6097.5 N/m² + ((821 kg/m³) * (2.78v_1)²)/2
solve for v_1
then
R = 2 pi (1.1)^2 * v_1
the pipe is horizontal
so no change in h
ρgh is equal on both sides
cancels out
now
v (velocity) is inversely proportional to square of radius
so
v_2 / v_1 = (r_1 )^2 / (r_2)^2 = 1.1^2 / 0.66^2 = 2.78
v_2 = 2.78 v_2
and
8130 N/m² + ((821 kg/m³) * (v_1)²)/2 = 6097.5 N/m² + ((821 kg/m³) * (2.78v_1)²)/2
solve for v_1
then
R = 2 pi (1.1)^2 * v_1
The rate of flow of oil in pipe has been 1.55 m/s.
Given,
The diameter of pipe, [tex]d = 0.985 \;\rm m[/tex]
The diameter of constriction, [tex]d' = 0.591\rm m[/tex]
The radius of horizontal pipe, [tex]r = 0.4925 \rm \;m[/tex]
The radius of constriction, [tex]r' = 0.2955 \;\rm m[/tex]
The density of oil, [tex]\rho = 821\;\rm kg/m^3[/tex]
Pressure in the pipe, [tex]P = 8100 \;\rm N/m^2[/tex]
Pressure at the constriction, [tex]P' = 6075\;\rm N/m^2[/tex]
Let v is the velocity of fluid in the pipe, and v' is the velocity of fluid at the constriction.
Computation for the rate of flow of oil
The equation of continuity has been given as:
[tex]r^2v=r'^2v'[/tex]
Substituting the values in the equation for relation of velocity as:
[tex](0.4925)^2v=(0.2955)v'\\0.2425v=0.0873v'\\v=0.36v'[/tex]
The relation between v and v’ has been [tex]v=0.36v'[/tex].
The Bernoulli’s equation for pressure has been given as:
[tex]P\;+\;\dfrac{1}{2} \rho v^2=P'\;+\;\dfrac{1}{2}\rho 'v'^2[/tex]
Substituting the values in equation as:
[tex]8100\;+\;\dfrac{1}{2} \;\times 821\;\times (0.36v')^2=6075\;+\;\dfrac{1}{2}\;\times 821\;\times v'^2\\2025\;+\;53.2\;v'^2=410.5v'^2\\2025=3565.8v'^2\\v'^2=5.675[/tex]
The velocity of oil in constricted pipe is 5.675 m/s.
The velocity of oil in horizontal pipe has been:
[tex]v=0.36v'\\v=0.36\;\times\;5.675\\v=2.04[/tex]
The velocity of oil in horizontal pipe has been 2.04 m/s.
The rate of flow (R) of oil has been given as:
[tex]R=\pi r^2v[/tex]
Substituting the values for rate of flow of oil in horizontal pipe:
[tex]R=3.14\;\times\;(0.4925)^2\times\;2.04\\R=1.55\;\rm m/s[/tex]
The rate of flow of oil in horizontal pipe is 1.55 m/s.
The rate of flow in constriction has been:
[tex]R=3.14\;\times\;(0.2955)^2\times\;5.675\\R=1.55\;\rm m/s[/tex]
The rate of flow of oil in pipe has been 1.55 m/s.
For more information about rate of flow, refer to the link:
https://brainly.com/question/24560420
