Reference no: EM132319872

Question 1: When the lake overflows, 1.21 x 10⁸ 1s^-1 of water exits the lake by flowing over the top of an overflow spillway such as that shown in Figure 3.

Figure 3 Overflow spillway on Claerwen Dam, Wales

i. Show that the mass of water leaving the lake in 1 second is 1.22 x 10⁸ kg (to 3 s.f.).

ii. The water from the reservoir flows down a river that can be modelled as an open channel. If the hydraulic diameter is 4.80 m, the wetted perimeter is 16.0 m, the slope is 0.008 and the Chezy coefficient is 5.00 m^0.5 s^-1, calculate the volumetric flow rate for this open channel flow (to 3 s.f.).

c. Using Figure 7(a) and assuming the cross-sectional dimensions of the long arm of the load-bearing frame are 7 mm by 5.82 mm (as in Figure 8. where α = 5.82 mm), confirm that the shear stress caused by the maximum shear force in the long arm is small when compared to the maximum bending stress.

For a shear force S acting over a cross-sectional area A. the shear stress τ is given by

τ = S/A

Calculate the maximum shear stress to three significant figures. Use CES EduPack to determine the value of the shear strength Ts and state the relative magnitude of the maximum shear stress compared with the maximum bending stress.

Question 2:

Lithium-ion batteries, such as that in Figure 9. occupy up to 30% of the space inside the load-bearing frame of smart mobile phones.

Figure 9 A lithium-ion battery in a mobile phone

a. Show that the maximum volume V of a battery that fits into 30% of the volume of the load-bearing frame shown in Figure 6(b) (and repeated below) is 1.09 x 10⁴ mm³ (to 3 s f.). Assume that the casing width a = 5.82 mm on all sides.

b. Increasing the specific charge (J kg^-1) of rechargeable batteries is one of the most sought after and highly researched topics in materials science and engineering.

A mobile phone battery has a specific energy. S_c = 0.82 MJ kg^-1 (see study session 1 2. The lithium battery'). Assuming the battery has a volume equal to the volume calculated in part (a) of this question and an average density of 1100 kgm^-3. Show that the maximum energy stored in the battery is 9.8 kJ (to 2 s.f.).

c. The manufacturer of a new mobile phone claims that a fully charged 3.7 V battery can maintain the phone in the standby mode (when it is not in active use) for up to 10 days. Show that the current used by the phone when in standby mode is 3.1 mA (to 2 s.f.).

d. Portable power banks are frequently used to charge mobile devices. Using your answer to part (b) of this question. Calculate the maximum theoretical number of complete charges of the mobile phone battery when using a 3 7V, 2000 mA h power bank.

e. Discuss why the actual number of charges is usually lower than the theoretical value. You should be able to answer Question 7(e) in no more than 50 words.

Question 3:

c. One of the bearings on a flywheel system is lubricated by oil. The bearing has a diameter of 28 0 mm and an axial length of 18.0 mm, with a radial clearance of 14.4 pm. The kinematic viscosity of the lubricating oil is 2.09 x 10^-5 m² s^-1 and the density is 835 kg m^-3.

If the power loss from the bearing is 1.34 kW, calculate the speed of rotation (in revolutions per minute) of the bearing. Give your answer to three significant figures and show all of your workings.

Attachment:- Question.rar