I Derivation of Fluid Pressure In A Gravitational Field

AI Thread Summary
The derivation of fluid pressure under gravity presented in the discussion contains a critical flaw regarding the assumption of uniform pressure over the volume. The equation used, P = 2ρgh, incorrectly implies that pressure is constant, which contradicts the principles of fluid mechanics. The value of h is misapplied, as it represents both the height for work done and a factor in volume calculations. This misunderstanding leads to an incorrect conclusion about fluid pressure. Accurate derivation must consider the variation of pressure with depth in a fluid.
bmarc92
Messages
8
Reaction score
0
Given that ##P = ρgh##, there's obviously a problem with the following derivation of fluid pressure under gravity. Can someone spot the flaw?

$$W = mgh$$
$$W = ρVgh$$
$$F \cdot dh = ρVgh$$
$$F \cdot dh = ρ(Ah)gh$$
$$F \cdot dh = ρgAh^{2}$$
$$\frac{d(F \cdot dh)}{dh} = \frac{d(ρgAh^{2})}{dh}$$
$$F = 2ρgAh$$

$$\frac{dF}{dA} = \frac{2ρgAh}{dA}$$
$$P = 2ρgh$$
 
Last edited:
Physics news on Phys.org
Your derivation assumes that the pressure is uniform over the volume V. This is not correct.
 
Thread 'Gauss' law seems to imply instantaneous electric field'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
Back
Top