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  • 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 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 Pneumatics

Week 2 Review Assignment

Problem 1

A rotary actuator has the following physical data:

Outer radius of rotor = 0.75 in

Outer radius of vane = 1.5 in

Width of vane = 0.75 in

If the torque load is 1000 in∙lb, what pressure must be developed to overcome the load?

Problem 2

A hydraulic motor has 7.5-in3 volumetric displacement. If it has a pressure rating of 1200 psi and receives oil from a 25-gpm theoretical flow-rate pump, find the motor

a. Speed

b. Theoretical torque

c. Theoretical horsepower

Problem 3

A hydraulic motor has a displacement of 165 cm3 and operates with a pressure of 98 bars and a speed of 1725 rpm. If the actual flow rate consumed by the motor is 0.0055 m3/s and the actual torque delivered by the motor is 210 N∙m, find

a. ηv

b. ηm

c. ηo

d. kW power delivered by the motor

Problem 4

A hydraulic transmission operating at 110-bars pressure has the following characteristics

__________________________________________

Pump motor____

VD = 65 cm3 VD = ?

ηv = 86% ηv = 93%

ηm = 92% ηm = 89%

N = 1740 rpm N = 550 rpm__

Find the

a. Displacement of the motor

b. Motor output torque

Problem 5

A pressure relief valve has a pressure setting of 850 psi. Compute the horsepower loss across this valve if it returns all the flow back to the tank from a 180-gpm pump. An unloading valve is used instead to unload the pump. If the pump discharge pressure during unloading equals 50 psi, how much hydraulic horsepower is being wasted?

Problem 6

The system shown below has a hydraulic cylinder with a suspended load W. The cylinder piston and the rod diameters are 2.5 in and 0.25 in respectively. The pressure relief valve setting is 1600 psi. Determine pressure p2 for a constant cylinder speed if

a. W = 575 lb

b. W = 0 (load is removed)

Figure for Problem 6

Problem 7

A double-acting cylinder is hooked up in the regenerative circuit shown. The relief valve setting is 110 bars. The piston area is 300 cm2 and the rod area is 65 cm2. If the pump flow is 0.0085 m3/s, find the cylinder speed and load-carrying capacity for the

a. Extending stroke

b. Retracting stroke

Problem 8

For the system shown (for the extension strokes of the cylinders), what pump pressure is required if the cylinder loads are 12000 lb each and cylinder 1 has a piston diameter of 6in?

Problem 9

a. Calculate the required size of a receiver that must supply air to a pneumatic system consuming 25 scfm for 12 min between 180 psi and 155 psi before the compressor resumes operation.

b. What size is required if the compressor is running and delivering air at 12 scfm?

Problem 10

Air at 110oF passes through a -in-diameter orifice having a flow capacity constant of 3.5. If the upstream pressure is 1500 psi, what is the maximum flow rate in units of scfm of air?

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MET230: Hydraulics and Pneumatics

Unit 2 Study Guide 1

Question 1

Which of the following statements is true about limited rotation hydraulic motors?

A. They are also called oscillating motors

B. They can rotate in both clockwise and counter clockwise direction

C. They are classified as rotary actuators

D. They rotate through less than one complete cycle

E. All of the above

Answer E. “All of the above”

Question 2

Which of the following statements list the main advantage (s) of gear motors?

A. Long expected life in all weather conditions

B. Highest overall efficiencies

C. Light weight

D. High power and torque at high speed

E. Low cost and from simple design

Answer E. “Low cost and from simple design”

Question 3

A. Volumetric efficiency is the theoretical flow rate the motor should consume, divided by the torque the motor should theoretically deliver.

B. Volumetric efficiency is the theoretical flow rate the motor should consume, divided by the actual power delivered to the motor.

C. Volumetric efficiency is the theoretical flow rate the motor should consume, divided by the actual flow rate consumed by the motor.

D. The volumetric efficiency of a motor can be greater than 1

E. None of the above

Answer C. “Volumetric efficiency is the theoretical flow rate the motor should consume, divided by the actual flow rate consumed by the motor.”

Question 4

Which of the following statements is true about different efficiencies of a hydraulic motor?

A. The overall efficiency of a hydraulic motor is, as in the case of pumps, equals to the product of the volumetric and mechanical efficiencies

B. The mechanical efficiency of a hydraulic motor is the inverse of that of a pump.

C. The volumetric efficiency of a hydraulic motor is the inverse of that of a pump.

D. A, B, and C

E. None of the above

Answer D. “A, B, and C”

Question 5

Which of the following statements is NOT true about different efficiencies of a hydraulic motor?

A. The volumetric efficiency of a hydraulic motor is the inverse of that of a pump.

B. The mechanical efficiency of a hydraulic motor is the inverse of that of a pump.

C. The overall efficiency of a hydraulic motor is, as in the case of pumps, equals to the product of the volumetric and mechanical efficiencies

D. Volumetric, mechanical, and overall efficiency of a motor are always greater the volumetric, mechanical, and overall efficiency of a pump respectively

E. None of the above

Answer D. “Volumetric, mechanical, and overall efficiency of a motor are always greater the volumetric, mechanical, and overall efficiency of a pump respectively.”

Question 6

Which of the following is true about hydraulic motors?

A. A motor uses more flow than it theoretically should

B. A hydraulic motor delivers less torque than it theoretically should

C. Hydraulic motors extract energy from a fluid and convert it to mechanical energy

D. In vane motors, vanes are held in contact with cam ring by springs or by being pressure-loaded

E. All of the above

Answer E. “All of the above”

Question 7

Which of the following is true about hydraulic motors?

A. A motor uses more flow than it theoretically should

B. A hydraulic motor delivers less torque than it theoretically should

C. Hydraulic motors extract energy from a fluid and convert it to mechanical energy

D. In vane motors, vanes are held in contact with cam ring by springs or by being pressure-loaded

E. All of the above

Answer E. “All of the above”

Question 8

Which of the following is true about hydraulic valves?

A. Directional control valves determine the path if a fluid in a given circuit

B. Pilot check valves can permit flow in the normally blocked opposite direction

C. A pressure relief valve is used to limits the maximum pressure in a hydraulic system

D. A pressure reducing valve is used to maintain reduced pressures

E. All of the above

Answer E. “All of the above”

Question 9

Which of the following is one way of actuating a directional control valve?

A. Solenoid actuated

B. Manually actuated

C. Piloted actuated

D. Mechanically actuated

E. All of the above

Answer E. “All of the above”

Question 10

Which of the following is true about hydraulic valves?

A. Directional control valves determine the path of a fluid in a given circuit

B. Pressure control valves protect the system against overpressure

C. Flow control valves control fluid flow rate in hydraulic circuit lines

D. Check valves permit fluid flow in only one direction regardless

E. All of the above

Answer E. “All of the above”

Question 11

Which of the following symbols represent a shuttle valve?

A.

B.

C.

D.

E. None of the above

Answer D.

Question 12

Which of the following symbols represent a two position, four-way directional control valve?

A.

B.

C.

D.

E. None of the above

Answer A.

Question 13

Which of the following is NOT a directional control valve?

A. Check valve

B. Shuttle valve

C. Solenoid actuated, spring return, two-position, three-way valve

D. Counterbalance valve

E. None of the above

Answer D. “Counterbalance valve”

Question 14

Which of the following is NOT a pressure control valve?

A. Pressure relief valve

B. Pressure reducing valve

C. Sequence valve

D. Unloading valve

E. None of the above

Answer E. “None of the above”

Question 15

Which of the following is NOT a flow control valve?

A. Needle valve

B. Non-pressure-compensated valve

C. Pressure compensated valve

D. Servo valve

E. None of the above

Answer D. “Servo valve”

Problem 1

A rotary actuator has the following physical data:

Outer radius of rotor = 0. 5 in

Outer radius of vane = 1.25 in

Width of vane = 1 in

If the torque load is 800 in∙lb, what pressure must be developed to overcome the load?

Solution

Known Data

Outer radius of rotor RR = 0.5 in

Outer radius of vane RV = 1.25 in

Width of vane L = 1 in

Torque T = 800 in∙lb

Unknown (s)

Pressure p?

Needed

Volumetric displacement VD

Formula

Detailed Calculation

First, solve for the volumetric displacement.

Then solve for the pressure that must be developed to overcome the load.

Problem 2

A hydraulic motor has 5-in3 volumetric displacement. If it has a pressure rating of 1800 psi and receives oil from a 10-gpm theoretical flow-rate pump, find the motor

a. Speed

b. Theoretical torque

c. Theoretical horsepower

Solution

Known Data

Volumetric displacement VD = 5 in3

Pressure p = 1800 psi

Theoretical flow rate QT = 10 gpm

Unknown (s)

a. Speed

b. Theoretical torque

c. Theoretical horsepower

Formula

Detailed Calculation

Problem 3

A hydraulic motor has a displacement of 120 cm3 and operates with a pressure of 100 bars and a speed of 2100 rpm. If the actual flow rate consumed by the motor is 0.0045 m3/s and the actual torque delivered by the motor is 180 N∙m, find

a. ηv

b. ηm

c. ηo

d. kW power delivered by the motor

Solution

Known Data

Volumetric displacement VD = 120 cm3 = 0.00012 m3

Pressure p = 100 bars = 10,000,000 Pa (N/m2)

Speed N = 2100 rpm = 35rev/s = 219.91 rad/s

Actual flow rate QA = 0.0045 m3/s

Actual torque TA = 180 N∙m

Unknown (s)

Volumetric efficiency ηV = ?

Mechanical efficiency ηm = ?

Overall efficiency ηo = ?

Formula

Detailed Calculation

Let’s start units conversion

Problem 4

A hydraulic transmission operating at 100-bars pressure has the following characteristics

__________________________________________

Pump motor____

VD = 105 cm3 VD = ?

ηv = 84% ηv = 93%

ηm = 91% ηm = 90%

N = 960 rpm N = 570 rpm__

Find the

a. Displacement of the motor

b. Motor output torque

Solution

Known Data

Pressure p = 100 bars = 10,000,000 Pa (N/m2)

Pump volumetric displacement VDP = 105 cm3 = 0.000105 m3

Pump volumetric efficiency ηVP = 84 % = 0.84

Motor volumetric efficiency ηVM = 93 % = 0.93

Pump mechanical efficiency ηMP = 91 % = 0.91

Motor mechanical efficiency ηMM = 90 % = 0.9

Pump speed NP = 960 rpm = 16 rev/s

Motor speed NM = 570 rpm = 9.5 rev/s = 59.69 rad/s

Unknown (s)

Motor volumetric displacement VDM =?

Motor output Torque Tby motor =?

Formula

Detailed Calculation

Problem 5

A pressure relief valve contains a poppet with a 0.7-in2 area on which system pressure acts. During assembly, a spring with a spring constant of 2200 lb/in is installed in the valve to hold the poppet against its seat. The Adjustment mechanism is then set so that the spring initially compresses 0.16 inches from its free-length condition. In order to pass full pump flow through the valve at the PRV pressure setting, the poppet must move 0.09 inches from its fully closed position. Determine the

a. Cracking pressure

b. Full pump flow pressure (PRV pressure setting)

Solution

Known Data

Poppet area Apoppet = 0.7 in2

Spring constant k = 2200 lb/in

Initial compression Sinitial = 0.16 in

Additional compression Sadditional = 0.09 in

Unknown (s)

a) Overall efficiency ηo?

b) Theoretical torque TT?

Needed

Theoretical flow rate QT?

Volumetric efficiency ηv?

Mechanical efficiency ηm?

Formula

Detailed Calculation

Problem 6

A pressure relief valve has a pressure setting of 2200 psi. Compute the horsepower loss across this valve if it returns all the flow back to the tank from a 23-gpm pump.

Solution

Known Data

Pressure p = 2200 psi

Back flow rate Q = 23 gpm

Unknown (s)

Horsepower loss HP?

Formula

Detailed Calculation

Problem 7

An unloading valve is used to unload the pump of problem 6. If the pump discharge pressure during unloading equals 32 psi, how much hydraulic horsepower is being wasted?

Solution

Known Data

Pump discharge pressure p = 32 psi

Flow rate Q = 23 gpm

Unknown (s)

Horsepower loss HP?

Formula

Detailed Calculation

Problem 8

A 1.5-in diameter sharp-edged orifice is placed in a pipeline to measure flow rate. If the measured pressure drop is 90 psi and the fluid specific gravity is 0.89, find the flow rate in units of gpm.

Solution

Known Data

Diameter D = 1.5 in

Pressure drop ∆p = 90 psi

Specific gravity SG = 0.89

Flow coefficient C = 0.8

Unknown (s)

Volume flow rate Q in gpm?

Needed

Orifice area A?

Formula

Detailed Calculation

Problem 9

The figure in front shows flow versus pressure drops curves for four valves when the fluid has a specific gravity of 0.89. What is the capacity coefficient of the valve identified by curve number 4 at a flow rate of 5 gpm?

Solution

Known Data

Specific gravity SG = 0.88

Flow rate Q = 5 gpm

Unknown (s)

Capacity coefficient CV?

Formula

Detailed Calculation

At a flow rate of 5 gpm the pressure drop for curve 7 is approximately 90 psi.

Hence,

Problem 10

The system shown below has a hydraulic cylinder with a suspended load W. The cylinder piston and the rod diameters are 1.75 in and 0.75 in respectively. The pressure relief valve setting is 700 psi. Determine pressure p2 for a constant cylinder speed if

a. W = 1800 lb

b. W = 0 (load is removed)

Figure for Problem 10

Solution

Known Data

Piston diameter DP = 1.75 in

Rod diameter Dr = 0.75 in

PRV set pressure = p1 = 700 psi

Load W = 1800 lb

Load W = 0 lb

Unknown (s)

Pressure p2?

Needed

Piston area AP?

Rod area Ar?

Formula

Detailed Calculation

Let’s first calculate the areas of the piston and the rod, then their difference.

For constant cylinder speed, the summation of forces on the hydraulic cylinder must equal zero.

Thus, we have

(a) W = 1800 lb

Solving,

(b)

Pressure p2 could have been calculated straight from the following symbolic expression

Obtained by solving the sum of forces acting on the cylinder equals to zero equation

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MET230: Hydraulics and Pneumatics

Unit 2 Study Guide 2

—————————————————————————————————-

Guidelines

1. Legibly write on each piece of paper, green engineering pad with grid on the back preferred

· Your first and last names

· The course and section number, if applicable

· The assignment number

· The page number

2. Clearly present

· The given data

· The unknowns

· The formulas needed, and

· Sketches, where applicable

3. Write only on one side of the paper

4. Draw a long solid line to separate two different consecutive exercises/problems

5. Use consistent units

6. Round off final answers to proper degree of precision or accuracy

7. Underline your final answer

8. Staple multiple pages (for in seat only)

———————————————————————————————————

Question 1

Which of the following is one of the three important considerations when analyzing or designing a hydraulic circuit?

A. Safety of operation.

B. Performance of desired function.

C. Efficiency of operation.

D. A, B, and C

E. None of the above

Answer D. “A, B, and C”

Question 2

Which of the following is the purpose of a regenerative circuit?

A. To regenerate the viscosity of the working fluid

B. To remove extra moisture from the working fluid

C. To speed up the extending speed of a double-acting cylinder

D. To control the temperature of the working fluid

E. None of the above

Answer C. “To speed up the extending speed of a double-acting cylinder”

Question 3

Which of the following is the purpose of fail-safe circuits?

A. Fail-safe circuits are designed to provide overload protection for system components

B. Fail-safe circuits are designed to regulate the flow rate of the working fluid

C. Fail-safe circuits are designed to control the bulk modulus of the working fluid

D. A, B, and C

E. None of the above

Answer A. “Fail-safe circuits are designed to provide overload protection for system components”

Question 4

Which of the following is one of the reasons for considering pneumatics instead of hydraulics?

A. Liquids exhibit greater inertia than do gases

B. Liquids exhibit greater viscosity than do gases

C. Hydraulic systems require special reservoirs and no-leak design components

D. There are no instances where pneumatics are considered instead of hydraulics

E. A, B, and C

Answer E. “A, B, and C”

Problem 1

A double-acting cylinder is hooked up in the regenerative circuit shown. The relief valve setting is 100 bars. The piston area is 120 cm2 and the rod area is 70 cm2. If the pump flow is 0.0018 m3/s, find the cylinder speed and load-carrying capacity for the

a. Extending stroke

b. Retracting stroke

Solution

Known data

Relief valve pressure p = 100 bars = 10,000,000 Pa

Piston area Ap = 120 cm2 = 0.012 m2

Rod area Ar = 70 cm2 = 0.007 m2

Pump flow rate Qp = 0.0018 m3/s

Unknown (s)

a. Extending stroke

· Cylinder speed VP ext?

· Load-carrying capacity Fload ext?

b. Retracting stroke

· Cylinder speed VP ret?

· Load-carrying capacity Fload ret?

Formula

Detailed calculation

Let’s start by converting units first

The cylinder extension speed VP ext, and extension load carrying capacity Fload ext can now be calculated as follow

Applying the formula related to the retraction, the cylinder speed VP ret, and load carrying capacity Fload ret are then found to be

Problem 2

For the system shown (for the extension strokes of the cylinders), what pump pressure is required if the cylinder loads are 4500 lb each and cylinder 1 has a piston area of 9 in2?

Solution

Known data

Cylinder 1 load F1 = 4500 lb

Cylinder2 load F2 = 4500 lb

Cylinder 1 piston area AP1 = 9 in2

Unknown (s)

Pump pressure p1?

Formula

Detailed calculation

Problem 3

For the meter-in flow control valve system shown, the following data are given:

Desired cylinder speed = 14 in/s

Cylinder piston diameter = 1.8 in (area = 2.545 in2)

Cylinder load = 2600 lb

Specific gravity of oil = 0.90

Pressure relief valve setting = 1100 psi

Determine the required capacity coefficient of the flow control valve.

( Hint: 1 gal = 231 in3 )

Solution

Known data

Cylinder speed vcyl = 14 in/s

Piston diameter = 1.8 in

Cylinder load Fload = 2600 lb

Specific gravity SG = 0.9

Relief valve pressure PPRV = 1100 psi

Unknown (s)

Capacity coefficient CV = ?

Formula

. From this formula we can extract,

Detailed calculation

The area of the piston is found to be

Replacing all the given values in the formula of the cylinder speed,

However, the units of Cv are , converting

It is worth notice that the Cv could also have been calculated straight from the formula

The conversion into units of done before gives the same answer of 0.992

Problem 4

Air is used at a rate of 40 cfm from a receiver at 90 oF and 140 psi. If the atmospheric pressure is 14.7 psia and the atmospheric temperature is 80 oF, how many cfm of free air must the compressor provide?

( Hint: o Rankine = oF + 460, psia = psig + 14.7 )

Solution

Known data

Let subscript 1 represent atmospheric conditions

V2 = 40 cfm

T2 = 90 oF = 90 + 460 = 550 oR

p2 = 140 psi = 140 + 14.7 = 154.7 psia

p1 = 14.7 psia

T1 = 80 oF = 80 + 460 = 540 oR

Unknown (s)

Volumetric efficiency ηv?

Formula

. Rewriting,

Detailed calculation

Units conversion was performed within “ known data” step.

Problem 5 Exercise 13-29E on page 505

a. Calculate the required size of a receiver that must supply air to a pneumatic system consuming 27 scfm for 10 min between 130 psi and 110 psi before the compressor resumes operation.

b. What size is required if the compressor is running and delivering air at 8 scfm?

Solution

Known data

Consuming rate Qr = 27 scfm

Supplying time t = 10 min

Maximum pressure pmax = 130 psi

Maximum pressure pmin = 110 psi

a) Output flow Qc = 0 scfm

b) Output flow Qc = 8 scfm

Unknown (s)

a) Receiver size without load Vr?

b) Receiver size with load Vr?

Formula

Detailed calculation

The solution is straight forward. Substituting the known data in the formula gives,

Problem 6

Determine the actual power required to drive a compressor that delivers air at 180 scfm at 110 psig. The overall efficiency of the compressor is 70%.

Solution

Known data

Flow rate Q = 180 scfm

Outlet pressure pout = 110 psig = 110 + 14.7 = 124.7 psia

Inlet atmospheric pressure pin = 14.7 psia

Overall efficiency ηo = 70 % = 0.70

Unknown (s)

Theoretical power HPTheor?

Actual power HPActual?

Formula

Detailed calculation

Pressure is to be expressed in absolute value. Hence, the inlet atmospheric pressure pin = 14.7 psia, and the outlet pressure pout = 110 psig = 110 + 14.7 = 124.7 psia.

Substituting given data into formulas,

Problem 7

Air at 115oF passes through a -in-diameter orifice having a flow capacity constant of 7. If the upstream pressure is 110 psi, what is the maximum flow rate in units of scfm of air?

( Hint: oRankine = oF + 460, psia = psig + 14.7 )

Solution

Known data

Upstream temperature T = 115 oF = 115 + 460 = 575 oR

Orifice diameter = ½ in

Flow capacity constant CV = 7

Upstream pressure p1 = 110 psi = 110 + 14.7 = 124.70 psia

Unknown (s)

Maximum volume flow rate Q = ?

Formula

Detailed calculation

Let’s start by converting temperature and pressure to absolute values.

The downstream pressure p2 is found to be

Substituting all the values in the flow rate formula gives

Problem 8

A single-acting air cylinder with a 2-in-diameter piston and 12-in stroke operates at 105 psig and reciprocates at 25 cycles per min. compute the air compensation in scfm of air.

Solution

Known data

Piston diameter DP = 2 in = 0.1667 ft

Stroke S = 12 in = 1 ft

Pressure p2 = 105 psig = 119.7 psia

Speed N = 25 cycle/min

Atmospheric pressure p1 = 14.7 psia

Unknown (s)

Air compensation Q1?

Needed

Piston Area AP?

Displacement volume VD?

Consumed flow rate Q2?

Formula

For constant temperature, this boils down to

Detailed calculation

As usual, let’s state by units conversion for the piston diameter DP, stroke S, and pressure p2

In order to determine the air compensation Q1, we need to first calculate the consumed flow rate Q1 which, requires a prior knowledge of the displacement volume VD. The latter cannot be known unless the piston are AP is evaluated first.

The consumed flow rate Q2 can now be calculate as

Finally, the air compensation Q1 is found to be

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