- #1

brotherbobby

- 700

- 163

- Homework Statement
- Water oozes out slowly from a pipe doubles back under the opening (spout) for a considerable distance and is held there by atmospheric pressure as shown in the figure below, before it detaches and falls. Four points are marked at the top and bottom of the water layers, inside and outside the pipe. Rank those four points according to the ##\mathbf{gauge\; pressure}## of the water there, the most positive first.

- Relevant Equations
- Gauge pressure to a liquid at a "depth" ##h## from the surface open to air : ##P_G = \rho_L gh ## where ##\rho_L## is the density of the liquid.

Assuming water to flow out of the pipe with the same speed as inside and the thickness of water column ##h_{ab} = h_{cd} = h##, my answer would be ##\mathbf{(P_b = P_c) > (P_a = P_d)}##.

My reasoning is as follows : at positions ##a\; \text{and}\; d## the gauge pressure is 0 and the total pressure is due to atmosphere (##P_{\text{atm}}##). Both the positions are on "top" of the column and open to air.

The gauge pressure at places ##b\; \text{and}\; c## is given by the formula above : ##P_G = \rho_L gh ##. As ##h## is the same for the two parts, the pressures are also the same.

**Is my answer correct?**