- Clearly present:
- The given data
- The unknowns
- The formulas needed, and
- Sketches, where applicable
- Use consistent units (Do not switch or convert between USCS and SI)
- Round off final answers to the proper degree of precision or accuracy (Use 3 decimal points or 3 significant digits for all your calculations and answers)
- Underline your final answer with proper unit
MET230 Hydraulics and Dynamics
Unit 1 Study Guide 1
Question 1
Which of the following is a component of a pneumatic system?
a. A compressor
b. An electric motor
c. An actuator
d. A valve
e. All of the above
Answer: e. “All of the above”
Question 2
Which of the following is true about fluid power?
a. A fluid power system uses a liquid to generate, control, and transmit power
b. Fluid power is another term for fluid transport
c. There is no difference between hydraulics or pneumatics fluid power systems
d. Power capacity of fluid systems is limited only by the physical strength of the material used for each component
e. None of the above
Answer: d. “Power capacity of fluid systems is limited only by the physical strength of the material used for each component ”
Problem 1
A hydraulic fluid has a specific weight of 58 lb/ft3. What is its specific gravity SG? What is its density ρ? ( Note: the specific weight of water is γwater = 62.4 lb/ft3, and the acceleration of gravity g = 32.2 ft/s2)
Known data
Fluid specific weight γfluid = 58 lb/ft3
Water specific weight γwater = 62.4 lb/ft3
Acceleration of gravity g = 32.2 ft/s2
Unknown (s)
Specific gravity SG?
Density ρ?
Formula
Solution
Problem 2
Ninety gallons of hydraulic oil weigh 691 lb. What is the specific weight γ in units of lb/ft3? ( Note: 1 gal = 0.1337 ft3)
Known data
Volume V = 90 gallons
Weight W = 691 lb
1 gal = 0.1337 ft3
Unknown (s)
Specific weight γ (lb/ft3)?
Formula
Solution
The volume need first to be converted from units of gallon to cubic foot
The specific weight can now be calculated as follow
Problem 3
A container weighs 4 lb when empty, 54 lb when filled with water, and 67 lb when filled with glycerin. Find the specific gravity SG of the glycerin.
Known data
Container weight when empty wempty = 4lb
Container weight when filled with water ww/water = 54 lb
Container weight when filled with glycerin ww/glycerin = 67 lb
Unknown (s)
Specific gravity SG of the glycerin?
Container volume V?
Formula
Solution
Water weight wwater = ww/water – wempty = 54 – 4 = 50 lb
Glycerin weight wglycerin = ww/glycerin – wempty = 67 – 4 = 63 lb
Problem 4
A cylindrical container has a diameter of 0.4 m and a height of 0.6 m. if it is to be filled with a liquid having a specific weight of 8360 N/m3, how many kg of this liquid must be added? ( Note: the acceleration of gravity in SI system is g = 9.81 m/s2)
Known data
Diameter D = 0.4 m
Height H = 0.6 m
Specific weight γ = 8360 N/m3
Acceleration of gravity g = 9.81 m/s2
Unknown (s)
Mass M in kg?
Needed
Cylindrical container cross sectional area Abase?
Cylindrical container volume V?
Density ρ?
Formula
Solution
The density and the volume need to be determined in order to calculate the mass.
To determine the volume of the cylindrical container, the cross section area must be found first,
The density is then calculated from the specific weight
The mass can now be calculated
Problem 5
Six liters of SAE 30 oil weighs 52.2 N. Calculate the oil’s
a. Specific weight
b. Density
c. Specific gravity
(Hint: acceleration of gravity g = 9.81 m/s2, specific weight of water γwater = 9810 N/m3)
Known data
Volume V = 6 liter
Weight = 52.2 N
Acceleration of gravity g = 9.81 m/s2
Specific weight of water γwater = 9810 N/m3
Unknown (s)
a. Specific weight γ?
b. Density ρ?
c. Specific gravity SG?
Formula
Solution
The volume need first to be converted from units of liter to cubic foot
Problem 6
Convert a -10 kPa (negative 10 kiloPascal) pressure to an absolute pressure in kPa. ( Note: the atmospheric pressure is Patm = 101 kPa)
Known data
Gauge pressure Pg = -10 kPa
Atmospheric Patm = 101 kPa
Unknown (s)
Absolute pressure Pabs =?
Formula
Solution
Problem 7
A hydraulic cylinder has a 250 mm diameter. How much oil pressure P (kPa) is required to produce 15000 N force at its piston?
Known data
Diameter D = 250 mm
Force F = 15000 N
Unknown (s)
Pressure P in kPa?
Formula
Solution
The diameter value is first converted from unit of mm to m
The area of the cylinder piston is found to be
The pressure P can now be calculated as
Problem 8
A 20-in3 sample of oil is compressed in a cylinder until its pressure is increased from 30 to 900 psi. If the bulk modulus equals 300,000 psi, find the change in the volume of the oil.
Known data
Volume V = 20 in3
Initial pressure p1 = 30 psi
Final pressure p2 = 900 psi
Bulk modulus β = 300,000 psi
Unknown (s)
Volume change ΔV?
Formula
Solution
The change in pressure is
The change in volume is therefore,
Problem 9
The load on a 3-in diameter hydraulic cylinder increases from 7,500 lb to 16,000 lb. Due to the compressibility of the oil, the piston retracts 0.01 in. if the volume of oil under compression is 30 in3, what is the bulk modulus of the oil in units of ksi (kilo psi)?
Known data
Diameter D = 3 in
Initial load F1 = 7500 lb
Final load F2 = 16000 lb
Height change ∆h = -0.01 in
Volume V = 30 in3
Unknown (s)
Bulk modulus β?
Needed (s)
Piston area A?
Volume change ΔV?
Load change ∆F?
Pressure change ∆p?
Formula
Solution
The cross section area A needs to be determined first
The change in the volume and pressure can now the calculated
Problem 10
An oil (SG = 0.91) has a viscosity of 205 SUS at 120 oF. Find the corresponding viscosity in units of cS (centiStokes) and cP (centiPoise).
Known data
Specific grav
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MET230: Hydraulics and Pneumatics
Week 1 Review Assignment
Problem 1
A hydraulic fluid has a specific weight of 60 lb/ft3. What is its specific gravity SG? What is its density ρ?
Problem 2
Eleven liters of SAE 30 oil weighs 92 N. Calculate the oil’s
a. Specific weight
b. Density
c. Specific gravity
Problem 3
Convert a -6 kPa (negative 6 kiloPascal) pressure to an absolute pressure in kPa.
Problem 4
A hydraulic cylinder has a 275 mm diameter. How much oil pressure P (kPa) is required to produce 12500 N force at its piston?
Problem 5
An oil (SG = 0.87) has a viscosity of 187 SUS at 120 oF. Find the corresponding viscosity in units of cS (centiStokes) and cP (centiPoise).
Problem 6
In the hydraulic jack shown, a force of 100 N is exerted on the small piston. Determine the upward force on the large piston. The area of the small piston is 65 cm2, and the area of the large piston is 950 cm2. If the small piston moves 12 cm, how far will the large move? Assume the oil to be incompressible.
Problem 7
The pneumatic/hydraulic system shown is use to lift a load. If the inlet air pressure is 450 kPa, determine the maximum load that can be lifted.
Problem 8
What is the theoretical flow rate from a fixed displacement axial piston pump with an eight-bore cylinder operating at 1750 rpm? Each bore has a 1.25-in diameter and the stroke of 0.75 in.
Problem 9
A vane pump is to have a volumetric displacement of 10 in3. It has a rotor diameter of 2in, a cam ring diameter of 4in, and a vane width of 2.5 in. what must be the eccentricity?
Problem 10
Problem 11
A gear pump has a 75-mm outside diameter, a 55-mm inside diameter, and a 30-mm width. If the actual pump flow rate at 2700 rpm and rated pressure is 0.0025 m3/s. What is the volumetric efficiency?
Problem 12
A pump has a displacement volume of 122 cm3. It delivers 0.0027 m3/s of oil at 1720 rpm and 85 bars. If the prime mover input torque is 175 N∙m
a. What is the overall efficiency of the pump?
b. What is the theoretical torque required to operate the pump?
Problem 13
A pump supplies oil at 25 gpm to a in diameter double acting hydraulic cylinder. If the load is 1800 lb (extending and retracting) and the rod diameter in, find the
a. Hydraulic pressure during the extending stroke
b. Piston velocity during the extending stroke
c. Cylinder horsepower during the extending stroke
d. Hydraulic pressure during the retracting stroke
e. Piston velocity during the retracting stroke
f. Cylinder horsepower during the retracting stroke
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MET230 Hydraulics and Dynamics
Unit 1 Study Guide 2
Question 1
Which of the following statements is true about positive displacement pumps?
a. Gear and vane pumps are the only two categories of positive displacement pumps
b. A positive displacement pump cannot be used with a pressure relief valve
c. The motion of a positive displacement pump cannot be reciprocating
d. The output flow rate varies with the system pressure
e. None of the above
Answer: e. “None of the above”
Question 2
Which of the following statements is true about dynamic pumps?
a. Dynamic pumps are self-priming
b. Centrifugal and axial pumps are not classified as dynamic pumps
c. Dynamic pumps are used for low-volume, high pressure applications
d. The flow rate output of dynamic pumps decreases as the circuit resistance increases
e. None of the above
Answer: d. “The flow rate output of dynamic pumps decreases as the circuit resistance increases”
Problem 1
What is the theoretical flow rate from a fixed displacement axial piston pump with a twelve-bore cylinder operating at 750 rpm? Each bore has a 1-in diameter and the stroke of 0.5 in.
Solution
Known data
Number of cylinder Y = 12
Rotational speed N = 750 rpm
Bore diameter D = 1 in
Stroke S = 0.5 in
Using Trigonometry:
Unknown(s)
Theoretical flow rate QT?
Needed
Piston/bore area A?
Displacement volume VD?D
Formula
Detailed Calculation
Problem 2
A vane pump is to have a volumetric displacement of 8 in3. It has a rotor diameter of in, a cam ring diameter of in, and a vane width of 1.75 in. what must be the eccentricity?
Solution
Known data
Volumetric displacement VD = 8 in3
Rotor diameter DR = 2.75 in
Cam ring diameter DC = 3.75 in
Vane width L = 1.75 in
Unknown(s)
Eccentricity e?
Formula
Detailed Calculation
Problem 3
Find the offset angle for an axial pump that delivers 22 gpm at 2000 rpm. The volumetric efficiency is 94%. The pump has a twelve 3/5 in diameter pistons arranged on a 4.75-in piston circle diameter
Solution
Known data
Actual flow rate QA =22 gpm
Rotational speed N = 2000 rpm
Volumetric efficiency ηV = 94% = 0.94
Number of cylinder Y = 12
Piston circle diameter D = 4.75 in
Piston diameter Dp = 3/5 in = 0.6 in
Unknown(s)
Offset angle θ?
Needed
Theoretical flow rate QT?
Piston area A?
Formula
Detailed Calculation
Problem 4
A gear pump has a 88.9-mm outside diameter, a 63.5-mm inside diameter, and a 31.75-mm width. If the actual pump flow rate at 2100 rpm and rated pressure is 0.0026 m3/s. What is the volumetric efficiency?
Solution
Known data
Outside diameter Do = 88.9 mm
Inside diameter Di = 63.5 mm
Width L = 31.75 mm
Rotational speed N = 2100 rpm
Actual flow rate QA = 0.0026 m3/s
Unknown(s)
Volumetric efficiency ηV?
Needed
Volumetric displacement VD?
Theoretical flow rate QT?
Formula
Detailed Calculation
We will start by units conversion first
In order to determine the volumetric efficiency ηV, we will need the volumetric displacement VD and the
theoretical flow rate QT
Problem 5
A pump has a displacement volume of 105 cm3. It delivers 0.0027 m3/s of oil at 1600 rpm and 69 bars. If the prime mover input torque is 145 N∙m
a. What is the overall efficiency of the pump?
b. What is the theoretical torque required to operate the pump?
Solution
Known data
Volumetric displacement VD = 105 cm3
Actual flow rate QA = 0.0027 m3/s
Rotational speed N = 1600 rpm
Pressure p = 69 bars
Applied torque T = 145 N∙m
Unknown(s)
a) Overall efficiency ηo?
b) Theoretical torque TT?
Needed
Theoretical flow rate QT?
Volumetric efficiency ηv?
Mechanical efficiency ηm?
Formula
Detailed Calculation
Let’s start by units conversion first
Now we can start the calculation
Problem 6
A pump supplies oil at 22 gpm to a in diameter double acting hydraulic cylinder. If the load is 1400 lb (extending and retracting) and the rod diameter in, find the
a. Hydraulic pressure during the extending stroke
b. Piston velocity during the extending stroke
c. Cylinder horsepower during the extending stroke
d. Hydraulic pressure during the retracting stroke
e. Piston velocity during the retracting stroke
f. Cylinder horsepower during the retracting stroke
( NOTE: for this exercise consider 1 ft3/s = 448 gpm)
Solution
Known data
Input flow rate Qin = 22 gpm
Piston diameter Dp = 1.75 in
Rod diameter Dr = 1 in
Extension force Fext = 1400 lb
Retraction force Fret = 1400 lb
Unknown(s)
EXTENSION
a) Hydraulic pressure pext
b) Piston velocity vext
c) Cylinder horsepower HPext
RETRACTION
d) Hydraulic pressure pext
e) Piston velocity vext
f) Cylinder horsepower HPext
Needed
Piston area Ap?
Rod area Ar?
Formula
EXTENSION
RETRACTION
Detailed Calculation
We will first convert the input flow rate unit from gpm to ft3/s
The calculation of the piston and rod area is next
Unknown variables can now be calculated
Problem 7
The inclined cylinder shown has a 2-in diameter piston. Determine the pressure required to extend the 4500-lb weight
Solution
Known data
Piston diameter Dp = 2 in
Inclination angle θ = 25o
Weight W = 4500 lb
Unknown(s)
Pressure p?
Needed
Longitudinal applied load Fload?
Piston area Ap?
Cylinder force Fcyl?
Formula
Detailed Calculation