Halliday, Resnick & Walker — Fluids: Problem Problem_88

Ship squat. When a ship travels through a shallow waterway, it can sink somewhat in what is known as ship squat because, as it advances, it forces water to flow underneath the hull, which reduces the water pressure there. In 1992, ship squat grounded the ocean liner Queen Elizabeth 2 near Martha’s Vineyard in ocean waters off Massachusetts. The ship’s draft in open water was 9.8 m but it grounded on a shoal at depth 10.5 m. Calculations about ship squat are very complicated and vary from one ship to another and from one waterway to another. Let’s consider a simplistic situation with a rectangular ship (Fig. 14.39). In open water, it has a draft (depth) of \( d = 9.80 \text{ m} \). (a) What is the gauge pressure \( p \) of the water just below the hull? (b) While moving through a shallow channel, water beneath the hull flows from bow to stern at \( 4.00 \text{ m/s} \). By how much is the pressure just below the hull reduced due to that flow? (c) What draft \( d' \) is then required to float the ship? (d) What is the magnitude of the ship squat?