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Show that the units for all 3 terms in bernouliis equation are the same 
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#1
Jan910, 05:14 AM

P: 34

1. The problem statement, all variables and given/known data
bernouliis equaton P + 1/2 Rho v^2 + Rho g h = constant find the units of the three terms on the left hand side & show they are the same and then the units of the constant on the right 3. The attempt at a solution all i can think to do here is check the SI units for each term units for pressure = Pa or NM^2 units for density = kg/m^3 units for velocity =m/s units for g = m/s units for h = m but i cant see how i combine them or how they all come out the same ? 


#2
Jan910, 07:26 AM

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P: 4,437

Pressure P = NM^2 = kg*M*s^2*M^2 = kg*M^1*s^2.
Similarly work out for the other two expression. You can see that all the tree terms have the same dimensions. 


#3
Jan910, 07:35 AM

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#4
Jan1110, 06:37 AM

P: 34

Show that the units for all 3 terms in bernouliis equation are the same
Ok so pressure becomes kgm^1 s^2, then the other terms expressed in
M , kg, s are ½ pv^2 is Kg m^3 m/s^1 Pgh is kg m^3 m/2^2 I think I am still having a problem with the powers thou, I am not combining the units correctly 


#5
Jan1110, 07:04 AM

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P: 41,310

What are the units for density? For v? 


#6
Jan1110, 11:03 AM

P: 34

density is mass / volume so its units are Kg m^3
for velocity units are m/s^1 so combined you get Kg m^3 m/s^1 and for the second part density  Kg m^3 units for g = m/s^2 units for h  m combines to give Kg m^3 m/s^2 i must be getting this wrong but i have re read my text book and i cant see where to correct it, 


#7
Jan1110, 11:09 AM

P: 671

The dimensions of velocity are [tex][L]^1\times [T]^{1}[/tex]
The dimensions of velocity squared are [tex][L]^2 \times [T]^{2}[/tex] 


#8
Jan1110, 11:27 AM

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P: 41,310

[kg*m^3]*[m*s^1]² = [kg*m^3]*[m*s^1]*[m*s^1] See if you can simplify that by collecting all the powers of m and s. (For example, what's m^3*m*m simplify to?) 


#9
Jan1210, 05:07 AM

P: 34

Ok I think I see it now,
So m^3*m*m simplifies to m^1 And s^1*s^1 simplifies to s^2 So the units for ½ρv² would be kg m^1s^2 Then for the second term Units for density are kg*m^3 Units for g are m*s^2 Units for h are m This is [kg*m^3]*[m*s^2]*[m] Collecting the m terms gives m^1 so the units are Kg m^1s^2 Then all I need is the units for the constant at the end, if the three terms all have the same units then the constant must be in the same units to the power 3, like if you have a volume then m*m*m the result is m^3 ? if so how do I do this for kg m^1s^2 ? 


#10
Jan1210, 05:12 AM

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P: 41,310




#11
Jan1310, 06:38 AM

P: 34

thanks so much for your help !!



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