Question

A four-stroke turbocharged \(V-16\) diesel engine built by GE Transportation Systems to power fast trains produces 4400 hp at 1500 rpm. Determine the amount of work produced per cylinder per ( \(a\) ) mechanical cycle and ( \(b\) ) thermodynamic cycle.

Short answer

Question: Calculate the work produced per cylinder per (a) mechanical cycle and (b) thermodynamic cycle for a V-16 diesel engine with a total power of 4400 hp and an engine speed of 1500 rpm. Answer: (a) The work produced per cylinder per mechanical cycle is 6152025 J. (b) The work produced per cylinder per thermodynamic cycle is 12304050 J.

Step-by-step solution

Find the total work produced by the engine

Given power, P = 4400 hp We need to convert this into Watts. $$ 1hp = 745.7 W $$ So, P = 4400 * 745.7 = 3281080 W Now, we need to find the work done in one minute, using the formula: W = P * t Since the engine rotates at 1500 rpm, time taken for one revolution is: $$ t = \frac{1}{1500} \, min $$ Therefore, the work done in 1 minute is: $$ W_{1min} = \, 3281080 \,\frac{J}{s} \cdot 60 \,s = 196864800 \, J $$

Find the work produced per cylinder

Since it is a V-16 engine, we have 16 cylinders in total. To find the work produced in one cylinder, we divide the total work done in 1 min by 16. $$ W_\text{per cylinder} = \frac{196864800 \,J}{16} = 12304050 \, J $$

Find the work produced per cylinder per mechanical cycle

For a four-stroke engine, one mechanical cycle consists of 2 engine revolutions or 720 degrees of crankshaft rotation. Therefore, work produced per cylinder per mechanical cycle is: $$ W_\text{mechanical cycle} = \frac{12304050 \,J}{2} = 6152025 \, J $$ Hence, the work produced per cylinder per mechanical cycle is 6152025 Joules.

Find the work produced per cylinder per thermodynamic cycle

For a four-stroke engine, one thermodynamic cycle consists of 1 engine revolution or 360 degrees of crankshaft rotation. Therefore, work produced per cylinder per thermodynamic cycle is: $$ W_\text{thermodynamic cycle} = 12304050 \,J $$ Hence, the work produced per cylinder per thermodynamic cycle is 12304050 Joules. In conclusion, the work produced per cylinder per (a) mechanical cycle is 6152025 J, and (b) thermodynamic cycle is 12304050 J.