# Overview

The is the Mechanical Engineering General AM Session. Questions are ordered from Q 001 through Q 040. Problems are in either S.I. or U.S. Customary Units.

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#### Question to Topic Map

Q 001–Q 012 | Basic Engineering Topics |

Q 013–Q 017 | Principles of Mechanical Systems and Materials |

Q 018–Q 020 | Applications of Mechanical Systems and Materials |

Q 021–Q 023 | Principles of Hydraulics and Fluids |

Q 024–Q 027 | Applications of Hydraulics and Fluids |

Q 028–Q 030 | Principles of Energy and Power Systems |

Q 031–Q 033 | Applications of Energy and Power Systems |

Q 034–Q 037 | Principles of HVAC and Refrigeration |

Q 038–Q 040 | Applications of HVAC and Refrigeration |

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## Q 001

Given the electrical circuit shown, which of the following statements is true?

- [A] V1 + V2 = IR1 + IR2 + IR3 + IR4
- [B] V1 / (R1 + R2 + R3) = V2 / R4
- [C] 1 / R1 + 1 / R2 + 1 / R3 = 1 / R4
- [D] Loop Resistance, Re = R1 + R2 + R3 + R4

## Q 002

An engineer deposits $20,000 in a savings account on the day his child is born. He deposits an additional $2000 on every birthday after that. The account has a 6% nominal interest rate, compounded continuously. How much money will be in the account the day after the child’s 21st birthday?

## Q 003

A graduating high school student decided to take some time off and work to save for college. Good for her. She decides to invest all money earned in a bond earning 6%, compounded quarterly.

The student hopes to save $10,000 by the time school stares in 12 months. How much money will she have to save each month?

## Q 004

A manufacturing production department operates 80 hrs a week. The process has a production rate of 45 units per hour, with a scrap rate of 1 out of 80 units.

With a 10% lost production allows, the number of good units that can be delivered per week is most nearly:

## Q 005

A build schedule for a multi-stage system consists of the following:

Task |
Description |
Follows Task |
Duration (days) |

If the manufacturing of parts from India is delayed by 4 days, now required 11 days to obtain the parts, the total completion delay is most nearly:

## Q 006

A machinist wants to create a hole for a 3/8-16 NC x 0.75 inch long countersunk screw. The dimensions of the hole and plates are shown in the figure. What is most nearly the value of dimension “h” so that the screw head will be flush with the part surface?

## Q 007

The minimum distance between the surface of Hole A and Slot B is most nearly.

## Q 008

A commercial product consist of a substrate and an active ingredient sold in drums. The active ingredient is sold in three different formulations.

The amount of Formulation 1 used per drum cannot exceed 3 lb and the amount of Formulation 2 used per drum cannot exceed 2 lb. The total cost of active ingredient cannot exceed $36 per drum.

Under these constraints, the largest number of units of active ingredient that can be added per drum is most nearly.

## Q 009

The voltage and the current across the 10 ohm resistor in the center leg is most nearly?

## Q 010

A firm uses an economic analysis to determine which of two different machines to purchase. Each machine is capable of performing the same task in a given amount of time. Assume the minimum attractive rate of return is 7%.

Parameter |
Machine X |
Machine Y |

What is the approximate equivalent uniform annual cost of machine X?

## Q 011

A firm uses an economic analysis to determine which of two different machines to purchase. Each machine is capable of performing the same task in a given amount of time. Assume the minimum attractive rate of return is 7%.

Parameter |
Machine X |
Machine Y |

What is the approximate equivalent uniform annual cost of machine Y?

## Q 012

A company produces a bearing that is commonly used by several OEM's who manufacture golf carts. The base cost of operation (rent, utilities, etc.) is $500,000 per year. The cost of manufacturing is $1.35 per bearing. The scrap rate is one bearing per 400. Each bearing sells for $8.00. How many must be made each year to break even, assuming each one made and meets spec is sold?

## Q 013

A metal alloy is need consisting of 75% pearlite and 25% ferrite when cooled at a slow rate from 2200 °F to room temperature. The metal that best meets this need is.

## Q 014

A 1 kg brick lays at rest on a broken shelf that has a slope of 35% relative to its horizontal base. What is most nearly the static coefficient of friction between the book and the shelf?

## Q 015

A cantilevered beam 40 m long is supported at its left end (Point A) and 8 m from its right end (Point B). The beam bears a uniform load of 20 N/m and a concentrated load of 600 N applied 6 m from its right end. What is most nearly the vertical shear acting on the beam at point C, which is 10 m from the left end?

## Q 016

A 1/4 inch diameter pipe hanger rod is loaded in tension with a 2,000 lb force. If the rod is 10 inch long and is made of the tensile tested material shown, the total elongation (inch) it will experience is most nearly.

## Q 017

A welded circular tube with a 0.03 inch wall thickness and a 0.50 outside diameter experiences periodic torque varying between -10 in∙lbf and 50 in∙lbf.

The tube is steel with a 42,000 psi yield strength and a 72,000 psi tensile ultimate strength. The tube endurance strength is 20,000 psi, and no stress concentrations exist. What is most nearly the factor of safety for infinite life fatigue loading?

## Q 018

A nickel alloy must be selected for an aircraft engine. It must support 28,000 psi at 1400 °F without yielding. Also, a strength-to-density ratio (psi / lbm / in^3) in excess of 100,000 and a strength-to-cost ratio (psi / $) of less than 350 is required. Properties of our four options are shown.

Nickel Alloy |
Yield Strength at 1400 °F (psi) |
Density (lbm / in^3) |
Cost ($ / lbm) |

What material best satisfies the given design specification?

##Q 019

A linear spring mass system consisting of a spring with a spring constant of 50 lbf/in and a mass of 25 lbm undergoes free vibration. The linear frequency (cycles/sec) of this vibration is most nearly:

## Q 020

The 3000 lbf load shown in the figure is supported by a beam that is secured by six 3/4-16 inch diameter bolts in a hexagonal array with neighboring bolts 4 inch apart.

What is the largest shear stress (psi) experienced by any one bolt?

## Q 021

The Mach number just upstream of a normal shock wave in air (k = 1.1) is 7.5. The Mach number downstream of the normal shock wave is most nearly:

## Q 022

The water level of a 15 psig pressurized tank is 8 ft below the water level of an open tank. A pump 15 ft below the water level of the open tank delivers water through schedule-40 steel pipe to the pressurized tank. The losses due to both pipe friction and fittings are 24 ft. The pump must have a total dynamic head in feet of water of most nearly:

## Q 023

A fan supplies 9000 cfm of air through a 240 ft long rectangular duct. The duct dimensions are 18 x 24 inches. If the duct has a friction factor of 0.07 and a roughness of 0.0003 ft, the total static pressure drop due to friction, in inches of water, is most nearly

## Q 024

Water at 20 °C flows through the pipe system, with a minimum ID of 19 mm. The flow rate is 300 L / min (0.30 m^3 / min). There are two 90 degree bends and one 45 degree bend in the system.

If the loss coefficients for the 90 degree elbows and 45 degree elbow are 1.5 and 0.4 respectively, what is most nearly the sum of the minor (head) losses (in meters) for the system?

## Q 025

Water at 60 °F flows through a 1 inch brass pipe (1.063 inch ID) at 7 fps. The Moody friction factor is 0.025. The pressure drop (psi) over a 100-ft length of this pipe is most nearly:

## Q 026

An engineer is pondering the addition of a diffuser to a tank exit. Refer to the figure. The exit velocity of the water without the diffuser and the sharp edge on the tank is 14.7 fps. With the diffuser, the flow rate of the system will increase, percentage wise, by most nearly

## Q 027

The system shown is used to test a 1750 rpm centrifugal pump. The line from the water tank to the pump is 10 ft of 3 inch schedule-40 steel pipe and an assortment of bends.

If the flow rate of the 80 °F water in the system is 1500 gpm and the head loss from all piping is 25 ft, the net positive suction head available (NPSHA) in feet is most nearly

## Q 028

A feedwater pump delivers 50 gpm water to a system. It has been specified that the water velocity in the pipe must not exceed 10 ft/sec given upstream pump limitations. What minimum size schedule 40 pipe (nominal) will carry the flow without exceeding the maximum velocity criteria?

## Q 029

Water in a supply tank is used to form a small fountain of water in a park. Twenty feet of 4 inch schedule 40 steel pipe contains four long radius 90 degree elbows and one open gate valve run from the bottom of the tank to the discharge point.

The opening in the tank has a sharp edge. If the minimum height that the 50 °F water must achieve is 8 ft, the minimum water depth, in feet, the tank needs to maintain is most nearly:

## Q 030

A 20 cubic foot tank holds 6 lbm of compressed nitrogen gas at 100 °F. Gas is released until the bottle pressure reaches 150 psi. What is most nearly the amount of gas released in lbm?

## Q 031

The turbines of a hydroelectric plant are placed 250 ft below the surface of the lake with a surface area of 300 square miles. There is no flow into the lake. The only outlet from the lake is through the turbines. At maximum power generation one turbine generates 190,000 kW, with the water from the turbine being discharged into the lake into a slow moving tailrace.

If the head loss though the intakes, penstock, and outlet works is 7 ft and there are 20 turbines in the plant generating maximum power, the least amount of time to lower the lake by 1 ft is most nearly:

## Q 032

In 2 hours, how much black-body radiation escapes a 3 cm by 2 cm rectangular opening in a kiln whose internal temperature is 900 °C?

## Q 033

A counterflow shell-and-tube heat exchanger is to be designed using 1 inch OD, 0.875 inch ID, 10 foot long tubing. 20,500 lbm/hr of water at 55 °F are used to cool 22,780 lbm/hr of a 95% ethyl alcohol solution (with a specific heat of 0.9 Btu / lbm - °F) form 160 °F to 110 °F.

If the overall heat coefficient of heat transfer based on the outer tube area is 50 Btu / hr - °F, then the number of tubes in the heat exchanger is most nearly:

## Q 034

Steam at 1200 °F enters a turbine that operates in a Rankine cycle. If the cycle operates between pressures of 1000 psia and 30 psia, the efficiency of the cycle is most nearly:

## Q 035

When running at full load, a chiller has the capacity to cool 200 gpm of water from 60 °F to 40 °F. If the rated coefficient of performance (COP) is 5.2, the total compressor heat that must be rejected to the cooling tower is most nearly.

## Q 036

8000 cfm of recirculated air from a room conditioned to 64 °F and 30% relative humidity are mixed with 4000 cfm of outdoor air at 90 °F db and 81 °F wb prior to entering a cooling coil system.

The humidity ratio (lbm of moisture per lbm dry air) of air entering the cooling coil system is most nearly:

## Q 037

A portable unit heater is used to heat a room with no windows. The 1200 ft^2 external wall is made up of 2 inch of polystyrene rigid insulation sandwiched between 8 inch brick and 5/8 inch gypsum board. Assume this composite structure has a heat resistance of 9.5 hr-ft^2-°F / Btu and that all heat flows through this interface.

The outdoor winter design temperature is 5 °F and the room is to be maintained at 78 °F. Using a 2x safety factor, the required heating capacity in kW for the unit heater is:

## Q 038

A refrigeration system of capacity of 2 refrigeration ton has a compressor work of 3.3 kW. The coefficient of performance of the system is most nearly:

## Q 039

A room contains equipment that consumes 5,000 W of power. In addition, 10 lbm/hr of water vapor is released into the room. The resulting cooling load (Btu / hr) is most nearly:

## Q 040

An environmental criterion for a museum requires 3000 ft^3 / min supply air to be delivered to a gallery space at 65 °F db and 51 °F wb. If the condition of the air leaving the cooling coil is 50 °F db and 52 °F wb, the reheat load is most nearly.