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Fundamental Question about Dynamic Pressure.

Fundamental Question about Dynamic Pressure.

Fundamental Question about Dynamic Pressure.

(OP)
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?

RE: Fundamental Question about Dynamic Pressure.

(OP)
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!

RE: Fundamental Question about Dynamic Pressure.

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

RE: Fundamental Question about Dynamic Pressure.

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

RE: Fundamental Question about Dynamic Pressure.

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

RE: Fundamental Question about Dynamic Pressure.


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 ρV2/2 (kinetic energy per unit mass of the Bernoulli equation) is divided by ρg, it results in V2/2g, and we obtain velocity head, with dimensions of length, m.

RE: Fundamental Question about Dynamic Pressure.

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

RE: Fundamental Question about Dynamic Pressure.

(OP)
Yeah, I got it.  I've really got to cut down on smoking crack.  winky smile

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