The author is right. There is atmospheric pressure at inlet and outlet.foo9008 said:Homework Statement
refer to part 8.2 in this problem , why P1 = P2 ?
http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Examples/eg6_ans.htmThe Attempt at a Solution
there's some elevation between inlet and outlet , how can P1 = P2 , is the author wrong ? [/B]
Chestermiller said:The author is right. There is atmospheric pressure at inlet and outlet.
In their analysis, they are also neglecting the elevation difference between inlet and outlet and also the weight of the fluid.
why the elevation difference between inlet and outlet can be neglected ?Chestermiller said:The author is right. There is atmospheric pressure at inlet and outlet.
In their analysis, they are also neglecting the elevation difference between inlet and outlet and also the weight of the fluid.
P1 and P2 are not atmospheric pressure as shown in the calculation , why P1 = P2?Chestermiller said:The author is right. There is atmospheric pressure at inlet and outlet.
In their analysis, they are also neglecting the elevation difference between inlet and outlet and also the weight of the fluid.
Because the static pressure difference between the inlet and outlet elevations is small compared to the pressure exerted on the surface of the blade, and the weight of the fluid in the control volume is small compared to force exerted by the blade to change the direction of the fluid jet.foo9008 said:why the elevation difference between inlet and outlet can be neglected ?
Look at the figure. P1 and P2 are both atmospheric. This isn't an enclosed tube. It's a jet open to the atmosphere.foo9008 said:P1 and P2 are not atmospheric pressure as shown in the calculation , why P1 = P2?
this is the(hand-written) question that i wish to ask , but then , i found the somewhat the same typed question on the internet , so i copy the link and ask here . ok , it's much clearer now .Chestermiller said:Because the static pressure difference between the inlet and outlet elevations is small compared to the pressure exerted on the surface of the blade, and the weight of the fluid in the control volume is small compared to force exerted by the blade to change the direction of the fluid jet.
We can calculate each of them and compare their magnitudes. The problem statement also inherently implies that you can neglect the elevation change, since it doesn't even give you the inlet and outlet elevations, and it assumes that the velocity and thickness of the jet doesn't change: "75mm wide and 25mm thick, strike the vane with a velocity of 25m/s."foo9008 said:this is the(hand-written) question that i wish to ask , but then , i found the somewhat the same typed question on the internet , so i copy the link and ask here . ok , it's much clearer now .
how do we know that the static pressure difference between the inlet and outlet elevations is small compared to the pressure exerted on the surface of the blade?
The pressure at point P1 and P2 are equal because of the principle of continuity, which states that the volume flow rate of an incompressible fluid is constant throughout a closed system. In other words, the same amount of fluid must pass through P1 and P2 in a given amount of time, resulting in equal pressures at both points.
The shape of the pipe has a direct impact on the pressure at P1 and P2. In a bent pipe, the fluid must change direction, which causes a change in velocity and pressure. This change in pressure balances out and results in equal pressures at both points.
Yes, the pressure at P1 and P2 is affected by the fluid's density. According to Bernoulli's principle, as the fluid flows through the bent pipe, its density remains constant, but its velocity changes. This change in velocity results in a change in pressure, which again balances out and results in equal pressures at P1 and P2.
In theory, the pressure at P1 and P2 can be unequal if the fluid is compressible or if there are external factors, such as obstructions or changes in elevation, that affect the flow and pressure. However, in a closed system with an incompressible fluid, the pressure at P1 and P2 will always be equal.
As mentioned before, changes in fluid velocity result in changes in pressure at P1 and P2. If the velocity increases, the pressure decreases, and vice versa. This relationship is described by the Bernoulli's equation, which states that as the velocity of a fluid increases, its pressure decreases, and vice versa.