1
$\begingroup$

I saw in a video that static pressure is simply hydrostatic pressure which is due to weight of fluid but when we see in venturimeter, fluid rises in capillary tube due to static pressure. My question is that why fluid rises up while static pressure is due to its weight and there shouldn't be pressure in uppermost point of flowing fluid?

$\endgroup$

1 Answer 1

1
$\begingroup$

Your understanding what is a static pressure term in the Bernoulli's equation is wrong. Considering this illustration :

enter image description here

Venturi effect in venturimeters measures static pressure differences between high and low cross-section points, namely :

$$ \rho g (h_{1}-h_{2})={\frac {\rho v_{2}^{2}}{2}}-{\frac {\rho v_{1}^{2}}{2}} \tag 1,$$

here $h_1,h_2$ are water column heights in a measuring tubes above baseline of a pipe. You have confused them with a depth (inside of pipe or a container). Of course elevation differences also makes contribution, but usually they can be ignored in most cases, as it is done deriving venturi effect from Bernoulli's principle.

So, as (1) equation shows- differences in static pressure are due to differences in dynamic pressure. If you would stop the flow, then dynamic pressure both terms would be equal 0, and accordingly this would result in measuring tubes fluid height equalization, namely $h_1=h_2$. In this case water level in a measuring tubes should drop to pipe baseline. Hence, main cause of venturi effect is dynamic pressure, and not the static one. Static one is just the consequence of dynamic, due to the Bernoulli's principle which says that these types of pressures must compensate each other.

$\endgroup$
3
  • $\begingroup$ Obviously according to bernoulis equation if static pressure decreases , dynamic pressure increases , but my question is that if weight is not responsible for static pressure than what contributes to static pressure $\endgroup$ Apr 11, 2023 at 15:57
  • $\begingroup$ Seems you didn't follow my argument. Static pressure can't change without a reason. It changes only as response to a dynamic pressure change. For example as in my given picture,- mass conservation of water says that volumetric flow rate $cm^3/1s$ should be same at each cross section of pipe. This gives rise to a greater flow speed in narrow pipe places (like pictured in the middle). Greater speed - is an attribute of greater dynamic pressure. This in turn summons a system response - lower static pressure at these narrow places. I.E. there is no static pressure without dynamic counterpart. $\endgroup$ Apr 11, 2023 at 18:54
  • $\begingroup$ Pressure change of object submerged inside of a fluid within depth $h$ is called hydrostatic pressure. That pressure is not the same as Bernoulli's laws "static pressure" term talks about. Above all things they also differ in $h$ sign,- hydrostatic pressure positive direction is down, while Bernoulli's laws static pressure positive direction is UP. I.e. the higher column in Venturi measuring tube will show a higher static pressure, while in hydrostatic pressure it's reverse - bigger depth shows higher hydrostatic pressure. $\endgroup$ Apr 11, 2023 at 19:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.