Tài liệu học tập
6 A 7500 tonne reinforced concrete lock structure has been constructed in a dry dock. The lock is 60m long by 30 m wide in plan and is shaped like an open shoe box. The side walls are 8 m high. (a) Will the lock structure ﬂoat in sea water of density 1025 kg/m3, and if so, what is its draught and free-board? (b) What additional weight will be required to sink the structure onto the sea bed if the depth of water is 5.3 m, assuming the structure is watertight? (c) If the additional weight is to be provided by a blanket of sand (density 2600 kg/m3), how thick must the layer of sand be? (1 tonne =1000 kg).
[(a) yes, 4.07 m, 3.93 m; (b) >22 352 ¥ 103N;(c) >0.5 m]
7 (a) Explain what is meant by a stratiﬁed ﬂuid. (b) A pressure transducer is used to measure the hydrostatic pressure on the sea bed in a tidal estuary. The water in the estuary is stratiﬁed at the point where the measurement is taken, with fresh water (1000 kg/m3) overlying saline water (1025 kg/m3). Water sampling shows that the fresh water extends from the water surface to a depth of 2.7 m. If the transducer indicates a gauge pressure of 69.73 ¥ 103N/m2, how thick is the layer of saline water?
8 In terms of displacement and buoyancy force, explain why a block of polystyrene ﬂoats but a brick does not.
9 When a pontoon is loaded with a heavy cargo it settles deeper in the water. Obviously the buoyancy force must increase to offset the additional weight, because the pontoon continues to ﬂoat. Explain why the buoyancy force increases by considering the hydrostatic pressure acting on the bottom of the pontoon.
10 An unloaded pontoon weighs 200 000 N and in plan is 12 m long by 7 m wide. It ﬂoats in sea water with a density of 1025 kg/m3. (a) What is the depth of immersion of the pontoon? (b) What is the distance between the centre of buoyancy (B) and the metacentre (M)?
[0.237 m; 17.245 m]