Task 3(i)
A model boat consists of an open topped, rectangular metal can containing sand as a ballast. If the can has a width of 100 mm, a length of 500 mm, and a mass of 1 kg, determine the mass of sand required for the can to be immersed to a depth of 250 mm in sea water (density of sea water = 1030 kg/m3).
You can assume that the can has a depth that exceeds the 250 mm (i.e. the water does not breach the rim of the boat).
Task 3(ii)
The velocity of water through a hosepipe of diameter 25 mm is found to be 300 kg/s.
a) What is the velocity of water in the hosepipe?
In order to water a newly seeded lawn, this velocity needs to be reduced to 200 m/s or less so that the seeds are not washed away. You have the tapered nozzle piece as seen in figure 1 available, which can be cut to the required length.
b) At what length should it be cut for watering the lawn?
Note: you can treat water as an incompressible fluid.
Figure 1: Tapered nozzle piece
Task 3(iii)
Research the methods that might be used to determine the density of a solid material and the density of a liquid.
Give a brief description of at least one common method for a solid and one for a liquid (brief means no more than 100 words for each).
Also note the particular benefits of each method (a maximum of three each) and any specific challenges (again, a maximum of three each). For example, "it has the benefit of being accurate, but it is expensive to carry out".
Don't forget to reference your research sources.
Task 4(i)
The amount that a particular metal will expand when heated can be calculated using the following equation:
e = αL(ΔT)
where:
e = expansion, or change in length (mm)
α = coefficient of thermal expansion (per °C)
L = Original length (mm)
ΔT = temperature difference (°C)
a) If the bronze rod in figure 2 is heated from 20°C to 80°C, by how much will its length increase?
Data - Bronze: α = 18 x 10-6 per °C, E = 117 GPa
Figure 1: Tapered nozzle piece
b) If the rod is rigidly held between two parallel faces, figure 3, which are 0.5 m apart, how much force will be exerted on the faces at the end of the heating process? (You can assume the faces are unaffected by the heating).
Figure 3
Task 4(ii)
A rigid container holds 1 kg of an ideal gas at a temperature of 20°C and pressure of 150 kPa. If the gas has Cv of 0.75 kJ/kgK calculate the heat transfer necessary to increase the temperature to 80°C and find the final pressure of the gas.
Task 4(iii)
An ideal gas at a pressure of 600 kPa and a temperature of 400 K expands adiabatically to a pressure of 150 kPa. Calculate the work done for each 1 kg of gas during the process if Cv = 0.815 kJ/kgK and y = 1.4.
Task 4(iv)
A steady flow device is insulated and operates with steam entering at a pressure of 600 kPa, a temperature of 300°C and a velocity of 150 m/s. Steam leaves the device as a saturated vapour at a pressure of 250 kPa with a velocity of 75 m/s. If there is no change in height across the device, the specific enthalpy of the steam is 2961 kJ/kg and of the vapour it is 2706 kJ/kg and the power input to the system is equivalent to 300 kJ/kg, calculate:
a) The work done for each kg of steam.
b) The efficiency of the system.