Question

The teapot effect:Water poured slowly from a teapot spout can double back under the spout for a considerable distance (held there by atmospheric pressure) before detaching and falling. In Fig. 14-23, the four points are at the top or bottom of the water layers, inside or outside. Rank those four points according to the gauge pressure in the water there, most positive first.

Short answer

The rank of the four points according to the gauge pressure in the water there, most positive first is$P_c<P_a=P_d<P_b.$

Step-by-step solution

The given data 

The figure shows the points where we have to find the gauge pressure.

Understanding the concept of the pressure

Using the concept of gauge pressure, we can see that the pressure value is proportional to the depth measured from the outer surface of the water.

Formula:

The gauge pressure at a depth on a body in downward direction, $P_g=\rho gh$ (i)

Calculation of the rank according to the pressure values

Gauge pressure is measured from the surface of the liquid.

We are measuring the gauge pressure from the surface of the tea spout as a reference level.

Thus, gauge pressure at each point is given using equation (i) as follows:

At point a:

$P_a=0$

At point d:

$P_d=0$

At point b:

Here, depth is downward.

Thus, the value of the pressure is given as:

$P_b=\rho gh$

At point c:

Here depth is measured upward. Hence,

$P_c=-\rho gh$

Therefore, the rank according to the gauge pressure in the water is$P_c<P_a=P_d<P_b.$