Consider two open water tanks, Tank X and Tank Y, both completely filled with water. Tank X has a stepped shape: its upper section is a cylinder of radius 2R and height h , while its lower section is a cylinder of radius R and height h . Tank Y is a uniform cylinder of radius R and total height 2h . If P_X and P_Y represent the hydrostatic gauge pressure at the bottom-most points of Tank X and Tank Y respectively, wh

Step-by-step solution

The hydrostatic gauge pressure at a depth H in a liquid of density is given by P = g H . It depends only on the vertical depth from the free surface and is independent of the shape of the container. For Tank X, the total vertical depth of water from the free surface to the bottom-most point is h + h = 2h . Therefore, the gauge pressure at the bottom of Tank X is: P_X = g (2h) For Tank Y, the total vertical depth of water from the free surface to the bottom-most point is 2h . Therefore, the gauge pressure at the bot