Mechanical Engineering Answers

A 40cm diameter pipe conveying water, branches into two pipes of diameter 30cm and 20cm respectively. If the average velocity in the 40cm diameter pipe is 3m/s. find the discharge in this pipe. Also determine the velocity in 20cm pipe if the average velocity in 30cm diameter pipe is 2m/s

A refrigerator works on the carnet cycle in temperature between -7°C and 27'C. It makes 500 kg of ice per hour at-5'C from water at 14'C. Find H.P required to drive the compressor and C.O.P. of the cycle. Take specific heat of ice as 2.1 KJ/Kg-k and latent heat as 336 kJ/Kg

An air refrigerator works between the pressure limit of 1bar and 5 bar. The temperature of the air entering the compressor and expansion cylinder is 10°C and 25°C. The expansion and compression follow the law of PV(13) C. Find the

following: 1) Theoretical COP of the refrigerating cycle

2) If the load on the refrigerating machine is 10 tons, then find the amount of air circulated per minute through the system assuming the actual COP is 50% of the theoretical COP

Assume L/D =1.5 and cp-1kJ/Kg °C and C=0.7

kJ/Kg °C for air

The natural frequency of vibration, in bending, of the wing of a military aircraft is found to be 20 Hz. Find the new frequency of bending vibration of the wing when a weapon, weighing 2000 lb, is attached at the tip of the wing, as shown in Figure. The stiffness of the wing tip, in bending, is known to be 50,000 lb/ft.

Using Holzer’s method, find the natural frequencies and mode shapes of the system shown in Figure, with m1 = 100 kg, m2 = 20 kg, m3 = 200 kg, k1 = 8000 N/m, and k2 = 4000 N/m.

One of the wheels and leaf springs of an automobile, traveling over a rough road, is shown in Fig. For simplicity, all the wheels can be assumed to be identical and the system can be idealized as shown in Fig. The automobile has a mass of m1 = 1000 kg and the leaf springs have a total stiffness of k1 = 400 kN/m. The wheels and axles have a mass of m2 = 300 kg and the tires have a stiffness of k2− 500 kN/m. If the road surface varies sinusoidally with an amplitude of Y = 0.1 m and a period of l = 6 m, find the critical velocities of the automobile.

Find the natural frequencies of the system shown on the right, with m1=m, m2=2m, k1=k, and k2=2k. Determine the response of the system when k=1000 N/m, m=20 kg, and the initial values of the displacements of the masses m1 and m2 are l and -1 respectively.

A machine tool, having a mass of 1000 kg and a mass moment of inertia of J0 = 300 kg-m2 is supported on elastic supports, as shown in Figure given below. If the stiffness of the support is given by 3000 N/mm and 2000 N/mm, and the supports are located at 0.5 m and 0.8 m, find the natural frequencies.

The roofing design consists of a retractable roof where the roof is opened using a shaft that is

connected to a motor. The motor of 1hp transmits power to a rotor at 1200rev/min. Neglecting any

transmission losses, determine the maximum shear stress in the shaft due to the same applied

torque, if the maximum shear stress in the shaft is limited to 2MPa. The external diameter of the

shaft is 0.05m and a wall thickness of 0.005m What will be the resulting angle of twist of the shaft,

due to the applied torque, over a length of 2.5m, given that the rigidity modulus, G=70GPa.

(1hp=745.7W)

The 96 prismatic lithium-ion battery cells were manufactured in Korea and the Scottish firm Axeon assembled them into a 1411-pound, 338-volt pack that provides a 71-kWh energy capacity and a claimed 1D miles of range [Note: replace D with your ID’s last two digits].

(d) Using the charge capacity of the battery derived in c, use dimensional analysis techniques to:

1.                 Determine the dimensions of Q using only mass, length and time.

2.                  Determine the equation that governs charging time of the battery.

3.                 If the charging current is 10 A. Find charging time assuming the values provided in c are valid values for part d.