Fundamental Question about Dynamic Pressure.

[PhilipFry]

Alright, I can't believe I need to ask this question, but I'm looking at the term in Bernoulli's equation for dynamic pressure (1/2*rho*velocity^2). Can someone explain to me the units on this this? When I look closely, it looks like it gives the answer as a unit of force, not pressure.

rho=density=kg/m^3
velocity=m/s^2

rho*velocity^2=kg/m^2*(m^2/s^2)=kg/ms^2=1 Newton!

What am I missing here?

 

[PhilipFry]

Oops, my fingers got ahead of me.

rho=density=kg/m^3
velocity=m/s

rho*velocity^2=kg/m^3*(m^2/s^2)=kg/ms^2=1 Newton!

 

[PhilipFry]

Ah, yes, I'm retared. I should turn in my degree.

 

[blackwed]

A Newton is a kg-m/sec^2.

 

[BronYrAur]

still not sure if you are clear. The units work out to (Kg-m)/(s-m)^2, or a Newton/m^2 --- pressure

 

[25362]

To PhilipFry,

As BronYrAur says 1 kg/(ms²) is a pressure unit = 1 Pascal = 1 Pa = 1 N/m². And as blackwed rightly says the unit of force (=mass[×]acceleration) 1 N = kg.m/s².

When [ρ]V²/2 (kinetic energy per unit mass of the Bernoulli equation) is divided by [ρ]g, it results in V²/2g, and we obtain velocity head, with dimensions of length, m.

 

[quark]

The unit what you got doesn't indicate either force or pressure, per se.

Force is either expressed in Newtons or Kgf
Pressure is either expressed in Newtons/m² or kgf/m²

What you got is a simplified unit and is kgm/(m.s²) and here kgm is kg mass (later on I will just use kg for kg mass).

Multiply and divide this with meters and you will get

kg x m/ (m x m x s²) = kg x m/(m² x s²)
by rearranging the terms,

(kg x m/s²)x(1/m²) = N/m², which is a pressure unit.

Fluid mechanics text books, use a constant gc when dealing with FPS system of units and express the dynamic head as rho*v²/2gc. Here, gc is 32.17 ft.lbm/lbf.sec²

This constant is not required for metric system as Newton is directly expressed as kg.m/sec². However, you can derive the pressure units for dynamic head by using the constant gc with units kg.m/N.sec²

 

[PhilipFry]

Yeah, I got it. I've really got to cut down on smoking crack. ;-)