Engineering Math and Equations

Question 1

Determine Pressure when a force of 200 lb is applied to an area of 4 sq in.

Answer 1

P = F/A P = 2OOlb / 4 sq in. P = 50 psi

Question 2

What is the area a 1500 lb force is acting on if it exerts a pressure of 100 psi?

Answer 2

A = F/P A = 707lb / 100 psi A = 7.07 sq in.

Question 3

What is the force on the bottom of a tank that has base dimensions of 6’ by 12’ and contains a water depth of 7” Note: feet must be converted to inches. There is a pressure of 0.433 psi per vertical foot (depth) of water.

Answer 3

F = P x A
F = (0.433 x 7) psi x [(6' x 12) x ( 12' x 12)} sq in
F = 3.031 psi x (72 x 144) sq in.
F = 3.031 psi x 10,368 sq in.
F = 31,425 lb

Question 4

What is the force on a flat head of a steam boiler drum (tube sheet) with a pressure of 100 psi and an area of 1000 sq in.

Answer 4

F = P x A
F = 100 psi x 1000 sq in.
F = 100,000 lb

Question 5

Define Work and it’s unit of measurement.

Answer 5

Work is the movement of an object by a constant force to a specific distance. The units of distance are stated in linear measurement (feet). Force is a push or pull measured in pounds (weight).

Question 6

Write the equation for work and unit of measurement

Answer 6

Work = Force x distance
W = F (in lb) x D (in ft)
W = F x D 
W = ft-lb

Question 7

Write equation for distance and force.

Answer 7

Distance = work/force
D = W/F
Force = Work/Distance
F = W/D

Question 8

How many ft-lb of work are done if a force of 80 lb is applied and moves an object 100’?

Answer 8

W = F x D
W = 80 lb x 100'
W = 8000 ft-lb

Question 9

How high is 2500 lb load lifted by a hoist performing 50,000 ft-lb work?

Answer 9

D = W/F
D = 50,000 ft-lb / 2500 lb
D = 20'

Question 10

What is the force applied to move an object if 450 ft-lb of work is done while moving this object 15’?

Answer 10

F = W/D
F = 450 ft-lb
F = 30 lb

Question 11

Define Power and its unit of measurement.

Answer 11

Power is the rate at which worked is performed.

The unit of measurement is ft-lb per unit of time.

Question 12

Write the equation for Power.

Answer 12

Power = Work / Time         P = ft-lb / T
Power = Force x Distance / Time

Question 13

Write the equation for Work.

Answer 13

Work = Force / Distance

Question 14

What is the power output of an engine that performs 140,000 ft-lb of work in 4 minutes.

Answer 14

P = W / T
P = ft-lb / T
P = 140,000 ft-lb / 4 min
P = 35,000 ft-lb / min

Question 15

Define mechanical HP.

Answer 15

1 mechanical HP = 33,000 ft-lb of work / minute

Horsepower = Power / 33,000 ft-lb / minute.

Question 16

How much horsepower will an engine develop if it does 168,000 ft-lb of work in 2.5 minutes?

Answer 16

HP = W / T x 33,000
HP = 168,000 ft-lb / 2.5 min x 33,000 ft-lb/min
HP = 168,000d ft-lb / 82,500 ft-lb
HP = 2.04 HP

Question 17

A pump delivers 2500 lb of water per minute and lifts it 280’. What is the horsepower of the pump?

Answer 17

HP = F x D / T x 33,000 ft-lb/min
HP = 2500 lb x 280' / 1 min x 33,000 ft-lb/min
HP = 700,000 ft-lb / 33,000 ft-lb
HP = 21.21 HP

Question 18

Write the equation do determine the quantity of latent added or removed from a substance.

Answer 18

Quantity of heat = Weight of substance x latent heat.
Q (in btu) = W (in lb) x Lh (in Btu/lb to change it state
Q = W x Lh

Question 19

How much heat is required to change 1000 lb of water to steam at 212 deg. F.

Answer 19

Q = W x Lh
Q = 1000 lb x 970.3 Btu/lb
Q = 970,300 Btu

Question 20

Write the equation to determine the quantity of sensible heat added to or removed from a substance.

Answer 20

Quantity of heat = Weight of substance x specific heat x (Final temp - Int. temp)
Q (in Btu) = W (in lb) x Sph (in Btu/lb/F x {T1 (in F) -T2 (in F)}
Q = W x Sph x (T1 - T2)

Question 21

How much heat transfer is required to raise the of 1000 lb of water from 92°F to 212°F

Answer 21

Q = W x Sph (T1 - T2)
Q = 1000 lb x 1 Btu/ln/°F x (212 - 92)°F
Q = 1000 lb x 120 Btu/lb
Q = 120,000 Btu

Question 22

Convert F to C

Answer 22

(1.8 x °C) to 32

Question 23

Convert ˚C to ˚F

Answer 23

˚F - 32 / 1.8

Question 24

1 Btu is equal to how ft-lb of mechanical energy

Answer 24

1 btu is equal to 778 ft-lb of mechanical energy.

Question 25

Write Eq. for Charles first laws

Answer 25

V1/T1 = V2/T2

Question 26

How many Btu/min are in 1 mechanical HP

Answer 26

42.4 Btu/min

Question 27

Write equation for Charles 2nd law.

Answer 27

P1/T1 = P2/T2

Question 28

What is the final volume of 10 cu ft. of gas @ 90˚F when heated to 200˚F at a constant pressure?

Answer 28

Answer is 12 cu ft. (pg. 14)

Question 29

What is the pressure on a gas tank with an initial temp. of 90˚F and a press. of 100 psi (85.3 psi) when heated to 200˚F.

Answer 29

P2 = 120 psia ( 105.3 psi)

Pg. 15

Question 30

Eq. for Boyle’s law

Answer 30

P1 x V1 = P2 x V2

Question 31

What is the final press. of 1 cu ft of air with an initial pressure of 100 psi that is expanded at a constant temperature to 2 cu. ft?

Answer 31

P2 = 50 psi (35.3 psig)

pg. 16