Verify the left-hand side of the equation below is dimensionless using the MLT system

Daniel S

Verify the left-hand side of the equation below is dimensionless using the MLT system.



I keep getting an additional "L" left over as do two of my friends.

My "solution",

D= Diameter = m => L
P= Pressure = N/m^2 = (M)(L^-1)(T^-2)
rho= Density = kg/m^3 = (M)(L^3)
V^2 = Velocity^2 = (m/s)^2 = (L/T)(L/T)

When I sub that back into the left hand side of the equation, it doesn't cancel (I'm probably making a silly mistake somewhere).

Coles

m.N.m.m.m.s.s/m.m.kg.m.m

N.s.s/kg

kg.m.s.s/kg.s.s

m

Are you sure it needs to be dimensionless?

Daniel S

Coles wrote: »

m.N.m.m.m.s.s/m.m.kg.m.m

N.s.s/kg

kg.m.s.s/kg.s.s

m

Are you sure it needs to be dimensionless?

Yes, it definitely has to be. I came across this solution:



I don't understand how they are getting M/(L^2.T^2), surely converting from N/m^2 we would end up with M/(L.T^2)?

Coles

Ah yes!

ΔPl is actually change in pressure per meter length! It's unit is N/m3

Link 7.1