Numerical Problems

200+ solved problems with step-by-step solutions

25
Problems Found
10
Basic
9
Intermediate
6
Advanced
Basic
Pattern Making
Problem #1: Pattern Size Calculation with Shrinkage Allowance

A steel casting has a final dimension of 200mm. Calculate the pattern size considering shrinkage allowance.

Intermediate
Solidification
Problem #2: Solidification Time Using Chvorinov's Rule

Calculate the solidification time for a cylindrical casting with diameter 100mm and height 150mm. Mold constant B = 2.5 min/cm².

Advanced
Gating System
Problem #3: Gating System Design - Cross-sectional Areas

Design a gating system for a casting requiring 5 kg of molten steel. Pouring time is 8 seconds. Calculate sprue, runner, and gate areas using 1:2:4 ratio.

Intermediate
Feeding System
Problem #4: Riser Volume Calculation

Calculate the riser volume required for a rectangular casting of dimensions 200×150×100mm. Use safety factor of 1.2.

Basic
Molding Sand
Problem #5: Sand Permeability Calculation

Calculate the permeability of molding sand if 2000 cm³ of air passes through a sand specimen of 50 cm² area and 5 cm height in 2 minutes at 10 cm of water pressure.

Basic
Arc Welding
Problem #51: Heat Input Calculation in Arc Welding

Calculate the heat input for arc welding with voltage 25V, current 150A, and welding speed 5 mm/s.

Basic
Process Parameters
Problem #52: Welding Speed Calculation

A welder completes a 300mm long weld in 4 minutes. Calculate the welding speed.

Intermediate
Consumables
Problem #53: Electrode Consumption Rate

Calculate the electrode consumption rate if 2.5 kg of electrodes are used to deposit 2 kg of weld metal in 3 hours.

Advanced
Heat Transfer
Problem #54: Thermal Efficiency in Welding

Calculate thermal efficiency if total heat input is 50 kJ and heat utilized for melting is 35 kJ.

Advanced
Weld Geometry
Problem #55: Penetration Depth Calculation

Calculate penetration depth using the empirical formula P = 0.1 × I^1.5 × V^0.5 × S^(-0.5) where I=200A, V=25V, S=60mm/min.

Basic
Cutting Parameters
Problem #101: Cutting Speed Calculation

Calculate the cutting speed for a 12mm diameter drill rotating at 1500 rpm.

Basic
Time Study
Problem #102: Drilling Time Calculation

Calculate the time required to drill a 25mm deep hole with feed rate 0.2 mm/rev at 800 rpm.

Intermediate
Productivity
Problem #103: Material Removal Rate in Drilling

Calculate the material removal rate for drilling with 15mm diameter drill, 0.25 mm/rev feed, at 1200 rpm.

Advanced
Forces
Problem #104: Thrust Force Calculation

Calculate thrust force using F = K × f^0.8 × D^1.2 where K=500, f=0.3 mm/rev, D=20mm.

Intermediate
Power Calculation
Problem #105: Power Requirement in Drilling

Calculate power required for drilling if MRR is 150 cm³/min and specific energy is 2.5 J/mm³.

Basic
Strain Analysis
Problem #151: True Strain Calculation

Calculate true strain when a specimen is stretched from 100mm to 125mm length.

Intermediate
Forging
Problem #152: Forging Force Calculation

Calculate forging force for a cylindrical billet with 50mm diameter, flow stress 300 MPa, and shape factor 1.5.

Advanced
Rolling
Problem #153: Rolling Force Calculation

Calculate rolling force for a strip 100mm wide, reduced from 10mm to 8mm thickness, with roll radius 250mm, friction coefficient 0.3, and mean pressure 200 MPa.

Intermediate
Extrusion
Problem #154: Extrusion Pressure Calculation

Calculate extrusion pressure for reducing a billet from 100mm² to 25mm² cross-section with flow stress 250 MPa.

Basic
Rolling
Problem #155: Reduction Ratio in Rolling

Calculate the reduction ratio when a plate is rolled from 15mm to 12mm thickness.

Basic
Grinding
Problem #201: Grinding Wheel Surface Speed

Calculate the surface speed of a grinding wheel with 200mm diameter rotating at 3000 rpm.

Intermediate
Grinding
Problem #202: Material Removal Rate in Grinding

Calculate MRR in surface grinding with work speed 30 m/min, feed rate 0.02 mm/pass, and depth of cut 0.05mm.

Intermediate
Grinding
Problem #203: Grinding Ratio Calculation

Calculate grinding ratio if 50 cm³ of workpiece material is removed and 2 cm³ of wheel is worn.

Advanced
Grinding
Problem #204: Contact Length in Grinding

Calculate contact length between grinding wheel and workpiece for wheel diameter 250mm and depth of cut 0.08mm.

Basic
Surface Quality
Problem #205: Surface Roughness Calculation

Calculate average surface roughness (Ra) for height deviations: 2, -3, 1, -2, 4 micrometers.