Mechanical Engineering Answers

3.) For some interest rate “i” and some number of interest periods “n” the uniform series capital

recovery factor is 0.3091 and the sinking fund factor is 0.1941.

1. Compute the interest rate.

2. If the interest rate i = 12% compounded annually, compute the capital recovery factor

for a period n = 5 years.

3. If the rate of interest i = 16% compounded quarterly what would be the sinking fund

factor for a period of 6 years.

Ans. 1. 11.5% 2. 0.27741 3. 0.02559

2.) In an ordinary annuity (uniform series of payments) if the nominal rate of interest is 8%

compounded quarterly for 6 years.

1. Compute the value of the capital recovery factor.

2. Compute the value of the sinking fund factor.

3. Compute the value of the present worth factor.

Ans. 1. 0.052871 2. 0.032871 3. 18.914

1.) For a uniform series of payments what is the value of

1. (F/A, 8%, 6) if it is compounded quarterly

2. (P/A, 6%, 8) if it is compounded semi-annually.

3. (F/A, 8%, 4) if it is compounded continuously.

Ans. 1. 30.42186 2. 12.5611 3. 4.528047

4.) An engineer is entitled to receive P25,000 at the beginning of each year for 18 years. If the rate of

interest is 4% compounded annually.

1. What is the present value of this annuity at the time he is supposed to receive the first

payment?

2. What is the sum of this annuity at the end of the 18th year?

3. Find the difference between the sum of this annuity which is paid at the beginning of

each year and an annuity paid at the end of each year.

Ans. 1. P329,141.72 2. P666,780.73 3. P25,645.41

A completely reversed axial load of 20 kN is applied to a machine finished plate (BS 080M50, HR) as shown in the figure. Determine the size b of the plate for indefinite cycle of operation based on Goodman equation. Consider b = 10d = 10t. Choose safety factor of 1.5 and reliability of 99%

A double riveted lap joint is made between 15mm thick plates. The rivet diameter and pitch are 25 mm and 75 mm, respectively. If the ultimate stresses are 400 MPa in tension, 320 MPa in shear and 640 MPa in crushing, find the minimum force per pitch which will rupture the joint. If the above joint is subjected to a load such that the factor of safety is 4, find out the actual stresses developed in the plates and rivets.

A plate 60 mm wide and 12.5 mm thick is to be welded to another plate by means of parallel fillet welds. The plates are subjected to a load of 80 kN. Find the length of the weld. Assume allowable shear strength to be 60 MPa.

calculate the energy transfer rate in w/m² across 6 in wall of firebrick with a temperature difference across the wall of 55°C. the thermal conductivity of the firebrick is 0.65 BTU/hr ft °F.

A spring has a natural length of 8 inches. If a force of 20 lb. stretches the spring 0.5

inches, find the work done in stretching from 8 inches to 11 inches

A horizontal "hot air blower" consists of a fan, an electrical heating element and a nozzle The power input to the fan is 50 J/s and the power input to the heating element is 1.44 kJ/s. The air enters the fan with negligible velocity at a pressure of 1 bar and a temperature of 20 C, the volumetric flow rate being 0.5 m3 /min. After passing over the heating element, the air leaves the nozzle with a velocity of 25 m/s and a pressure of 1.1 bar. Treating the complete arrangement as a steady flow system and ignoring any heat loss from the system, determine: (a) The mass flow rate of air entering the fan in kg per second (b) The kinetic energy of the air leaving the nozzle per second (c) The change in enthalpy of the air occurring per second between entering the fan and leaving the nozzle (d) The temperature of the air as it leaves the nozzle. (e) The density of the air as it leaves the nozzle (f) The flow area at the nozzle exit. Take R = 0.287 kJ/kgK and cp = 1.005 kJ/kgK