Task 1: A rectangular tank is filled to the brim with water. On one of the sidewalls, there is a flap door that has a hinge at the bottom of the tank (see Figure 1). a) Calculate the force acting on the flap door (due to the hydrostatic pressure.. b) Calculate the overturning moment acting on the flap door. Flap door 0.88m Hinge Figure 1: Water tank 0.58mTask 2: Archimedes' principle enabled the study of material density and plays an important role when designing ships or submarines. You are provided with a basic model "ship" (see Figure 2). a) Explain Archimedes' principle using your own words (you may also use sketch es). b) Calculate volume of the water displaced by the model and the upthrust on the hull of the model. c) Describe and compare two methods that might be used to 0.25m determine the density of an irregularly shaped piece of material. 0.8m Task 3: Figure 2: Model ship 42 0.5mAn electric shower provides warm water by heating up cold water as it flows through heating elements (see Figure 3). Cold water (Ti = 16 'C) flows through a supply pipe with diameter of 18mm with a velocity in of 0.19m/s. The water is led through a tapered pipe to a larger pipe of diameter of 48mm, where it meets the heating elements. Afterwards, the water has a temperature out of 31. C. a) Calculate the flow rate in of the water. b) Calculate the speed of the water out at the end of the tapered pipe. c) Calculate the efficiency of the shower, given that the power rating of the shower is 10.5kW. Heating Vout elements Vin od= 18 mm EO 048 Tin = T out 16 C Figure 3: Pipe system for heating waterTask 4: The manufacturing of ships (and shipyards) commonly involves the casting of large structures. You are asked to calculate the energy it takes to melt a block of cast iron in a furnace. The iron starts off at a room temperature of Tr = 20 C, with a melting temperature of 1204 'C, specific heat coefficient of 460 J/kg K and latent heat of 126000j/kg. a) Calculate the total energy it takes to melt the block of cast iron with a mass 890KG. Task 5: The structural integrity of a ship relies (among many other factors) on steel struts incorporated in the design. During the engine's operation, the steel is subject to heating. The steel strut is at a temperature of To = 5"C at the beginning and has a linear thermal expansion coefficient of a = 17.3 x 10-6 . The modulus of elasticity is E = 200GPa. a) Calculate the lengthening of a strut when its original length is 3.6m and it is heated to a temperature of 32.C. b) If the strut is rigidly fixed at both ends, it cannot expand. Instead, the material is subject to stress. Calculate the stress and force acting on the strut; assuming the strut has a cross- section area of 0.12m2. Task 6: Piston engines, for example petrol or diesel engines, use the compression and expansion of gas in a cylinder to produce work. Consider a cylinder from a large ship engine with an internal diameter of 0.8m. The piston has a stroke length of 1.2m. As the piston travels downwards to the end of the cylinder it draws the air into the chamber at 20'C and at atmospheric pressure. Afterwards, the air is compressed within the cylinder. a) Calculate the mass of the gas transferred in one stroke. The specific gas constant of air is R = 287 J.kg-1.K-1. b) On the up-stroke, the piston compresses the air to 1/12 of the original volume. During this compression, the temperature of the air rises to 6850C. Calculate the pressure of the compressed air at this stage