Re: Fluid pressure in a tube of variable diameter

Hi Tim,

The Bernoulli Equation is basically a statement of the conservation of 
energy principle for flowing fluids. The "Bernoulli effect" is the 
lowering of fluid pressure in regions where the flow velocity is 
increased. This lowering of pressure in a constriction of a flow path may 
seem counterintuitive but seems less so when you consider pressure to be 
energy density. In the high velocity flow through the constriction, 
kinetic energy must increase at the expense of pressure energy.

Now there is also an effect linked to Poiseuille's Law which means that 
there is going to be a pressure difference between the start and the end 
of the tube (a bit like a potential difference across a wire in an 
electric circuit) caused by the viscous resistance between the fluid and 
the wall.

So the pressure at the end of the tube would be slightly less than at the 
start but in the middle, where the tube is wider, the pressure will 
increase slightly due to the slower speed of the fluid (and hence less 
kinetic energy, giving more pressure energy).

Hope this helps!

Keith
Wales
United Kingdom