Pressure difference in decreasing diameter tube

[MonkeyMouse]

Homework Statement

Helium at 20°C passes through a pipe with an initial diameter of .3 meters decreasing to .25 meters. The helium flows at .30 kg/s and an initial pressure of 200 kpa. Find the difference in pressure ΔP across the decreasing section. Assume incompressible and inviscid flow.

From known values of helium at 20°C: Density= 0.166 kg/m³, Specific weight= 1.63 N/m³,

Homework Equations

Bernoulli eq: (p₁/$\gamma$)+(V₁²/2g)+Z₁=(p₂/$\gamma$)+(V₂²/2g)+Z₂

V=Q/A

The Attempt at a Solution

Not a free jet situation.
Z₁ and Z₂ = 0 due to no elevation change

A₁=($\pi$.3m²)/4=.0706m²
A₂=($\pi$.25m²)/4=.0491m²

My hang up is when I get to this point, Q=.30 Kg/s and I am unsure how to convert this to m³/s in order to find V₁ and V₂ in terms of m/s? Also once I have this I am unsure of the unit conversions I would need to return P₂ in kpa in order to find the pressure difference?

 

[SteamKing]

Homework Statement

Helium at 20°C passes through a pipe with an initial diameter of .3 meters decreasing to .25 meters. The helium flows at .30 kg/s and an initial pressure of 200 kpa. Find the difference in pressure ΔP across the decreasing section. Assume incompressible and inviscid flow.

From known values of helium at 20°C: Density= 0.166 kg/m³, Specific weight= 1.63 N/m³,

Homework Equations

Bernoulli eq: (p₁/$\gamma$)+(V₁²/2g)+Z₁=(p₂/$\gamma$)+(V₂²/2g)+Z₂

V=Q/A

The Attempt at a Solution

Not a free jet situation.
Z₁ and Z₂ = 0 due to no elevation change

A₁=($\pi$.3m²)/4=.0706m²
A₂=($\pi$.25m²)/4=.0491m²

My hang up is when I get to this point, Q=.30 Kg/s and I am unsure how to convert this to m³/s in order to find V₁ and V₂ in terms of m/s? Also once I have this I am unsure of the unit conversions I would need to return P₂ in kpa in order to find the pressure difference?

You use the continuity relation and assume that the volume of helium flowing into the pipe is the same as the volume flowing out of the pipe. Since the helium is assumed incompressible, the density is constant in the pipe. You know the cross-sectional area of the pipe, so you should be able to calculate the flow velocity of the helium which satisfies the continuity relation thru the pipe.

 

[MonkeyMouse]

what if your required to use Bernoullis eq? Would you divide the mass flow by the density for the volumetric flow to solve for velocity?

There for: (0.30kg/s)/(0.166kg/m^3)=1.807m^3/s

 

[Chestermiller]

what if your requied to use Bernoullis eq? would you decide the mass flow by the density for the volumetric flow to solve fir velocity?

Sure. Why not?

 

[SteamKing]

what if your requied to use Bernoullis eq? would you decide the mass flow by the density for the volumetric flow to solve fir velocity?

Using Bernoulli does not necessarily mean that the continuity relation is invalid. After all, Bernoulli relates the total energy of the flow at one point to another. All the continuity relation does is state that fluid is not created or destroyed between these same points. Both relations are complementary.

 

[MonkeyMouse]

Has anyone worked, or could anyone work through this problem? I'm coming up with an increase of 58 Pa which seems low?