The discussion revolves around the applicability of the hydrostatic pressure equation, \( p = p_{atm} + \text{density} \cdot g \cdot h \), in fluid dynamics, particularly in the context of Bernoulli's equation and the behavior of fluids under various conditions.
Participants express differing views on the validity of the hydrostatic pressure equation in fluid dynamics, with some arguing for its applicability under specific conditions while others maintain that it is not generally valid. The discussion remains unresolved regarding the derivation of the hydrostatic pressure equation from Bernoulli's theorem.
Participants mention various assumptions and conditions, such as fluid viscosity, flow type, and velocity, which affect the applicability of the equations discussed. The relationship between the terms in Bernoulli's equation and their interpretations is also a point of contention.
vijayramakrishnan said:in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?
thank you for replying sir,but it doesn't provide any direction relation between height and pressure?Dr. Courtney said:Look up the Bernoulli equation.
No. The same equation is not generally valid in fluid dynamics. The fluid dynamics of viscous fluids is described by the much more complicated Navier Stokes equations.vijayramakrishnan said:in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?
vijayramakrishnan said:thank you for replying sir,but it doesn't provide any direction relation between height and pressure?
Chestermiller said:No. The same equation is not generally valid in fluid dynamics. The fluid dynamics of viscous fluids is described by the much more complicated Navier Stokes equations.
and also incompressiblevijayramakrishnan said:thank you for replying sir,but we can assume the fluid to be non viscous and flow to be streamline
thank you for replying sir,i read that article and it was indeed helpful,and i know what is bernoulli's equation, but all i want to know is can we apply the theorem that pressure = density*g*h in fluid dynamics?for example we have used it in rotating fluids to determine the shape of free surface of liquid but can we do the same if the liquid is moving?or is that equation necessarily not valid in fluid dyanmics?if yes then why so? we use Newton's laws to derive that but if the fluid is moving with uniform velocity it has no acceleration so why can't the same law be applied here?boneh3ad said:Given your criteria you've now laid out, what was wrong with the Bernoulli answer? Take a look at the link provided by @spamanon.
sir,i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem.please help.russ_watters said:I'm not sure how many ways people can say "yes" before you will take it, but yes, given all of those constraints and the constant velocity constraint, yes, Bernoulli's equation basically reduces to the hydrostatic pressure equation.
vijayramakrishnan said:sir,i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem.please help.
sir,so does the third term represent the hydrostatic pressure?boneh3ad said:You do see that there is a ##\rho g z## term in Bernoulli's equation, right? Bernoulli's equation is essentially an energy balance cast in terms of pressure, where each side of the equation (i.e. each ##p + \frac{1}{2}\rho v^2 + \rho g z## term) constitutes what is commonly called total pressure. One element of that is the hydrostatic pressure.
vijayramakrishnan said:sir,so does the third term represent the hydrostatic pressure?
I don't understand. You were instructed to look up Bernoulli's equation. Did you? Every source describing it should list the meaning of each term. What did your research say?vijayramakrishnan said:sir,so does the third term represent the hydrostatic pressure?
vijayramakrishnan said:i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem