Some Illustrative Example Problems

 some illustrative example problems: Fluid Power Priniciples and Hydraulic Pumps - Hydraulics and Pneumatics

SOME ILLUSTRATIVE EXAMPLE PROBLEMS

Problems On Gear Pumps

Example 4.1 

A gear pump has a 80 mm outside diameter, a 55 inside diameter, and a 25 mm width. If the actual pump flow at 1600 rpm and rated pressure is 95 Lpm, what is the volumetric efficiency ?

Given Data: 

D0 = 80 mm; Di = 55 mm; L = 25 mm; N = 1600 rpm;

Rated pressure = 95 Lpm.

Solution: It is given that rated pressure is 95 Lpm (i.e., litres per minute). That means, the actual discharge,

QA = 95 Lpm = 95 × 10-3 m3/min  [⸪ 1 L = 0.001 m3]

We know that the volumetric displacement of the gear pump,

Example 4.2 

A gear pump has a 75 mm outside diameter, 50 mm inside diameter and a 25 mm width. If the volumetric efficiency is 90% at rated pressure, what is the corresponding actual flow rate? The pump speed is 1000 rpm. 

Given Data: 

Do = 75 mm; Di = 50 mm; L = 25 mm; ηvol = 90%; N = 1000 rpm 

Solution: We know that the volumetric displacement of the gear pump,

We also know that,

Example 4.3

Calculate the actual delivery of a gear pump for the following specifications: Module of gear teeth 6 mm; Number of teeth in driver gear = 18; Gear width = 25 mm; Pressure angle = 20°; Pump speed = 1000 rpm; Volumetric efficiency = 90%.

Given Data: 

m = 6 mm; z 18; L = 25 mm; α = 20°; N = 1000 rpm; ηvol =  90%. 

Solution: We know that the theoretical discharge of a gear pump,

Problems on Vane Pumps

Example 4.4

A vane pump is to have a volumetric displacement of 95 cm3. It has a rotor diameter of 60 mm, a cam ring diameter of 85 mm, and a vane width of 50 mm. What must be the eccentricity?

Given Data: 

VD = 95 cm3 = 95 × 10-6 m3; DR = 60 mm; DC = 85 mm; L = 50 mm.

Solution: We know that the volumetric displacement of the vane pump,

Problems on Piston Pumps

Example 4.5 

Find the offset angle for an axial piston pump that delivers 1.25 Lps at 2000 rpm. The pump has nine 12.7 mm diameter pistons arranged on a 130 mm diameter piston circle. The volumetric efficiency is 94%.

Given Data: 

QA = 1.25 Lps = 1.25 × 10-3 m3/s = (1.25 × 10-3) × 60 = 0.075 m3/min; N = 2000 rpm; Y = 9; d = 12.7 mm; D = 130 mm; ηvol = 94%.

Solution: We know that the theoretical discharge of an axial piston pump,

QT = D A N Y tan θ m3/min

Then the actual discharge,

Substituting in equation (1), we get

Example 4.6

Calculate the actual flow rate in units of Lps of a radial piston pump for the following specifications:

Number of pistons = 9; Diameter of piston = 25 mm; Maximum eccentricity = 10 mm; Speed of rotor = 1800 rpm; Volumetric efficiency = 95%.

Given Data: 

Y = 9; d = 25 mm; e = 10 mm; N = 1800 rpm; ηvol = 95%.

Solution: We know that the theoretical discharge of a radial piston pump,

QT = 0.5 e Y π d2 N m3/min

= 0.5 × 0.01 × 9 × π (0.025)2 × 1800 = 0.159 m3/min

Then the actual delivery,

Problems on Pump Efficiencies

Example 4.7 

A pump of positive displacement type has a mechanical efficiency of 94% and a volumetric efficiency of 92%. What is its overall efficiency?

Given Data: ηmech = 94%; ηvol = 92%.

Solution: We know that,

Example 4.8 

A pump has a displacement of 98.4 cm3. It delivers 0.00152 m3/s at 1000 rpm and 70 bar. If the prime mover input torque is 124.3 N-m,

(a) Find the overall efficiency of the pump.

(b) What is the theoretical torque required to operate the pump? 

Given Data: 

VD = 98.4 cm3 = 98.4 × 10-6 m3; QA = 0.00152 m3/s; N= 1000 rpm; P = 70 bar = 70 × 105 N/m2; T = 124.3 N.m.

Solution:

(a) To find overall efficiency of the pump (ηo) :

We know that the volumetric efficiency of a pump,

(b) To find the theoretical torque required to operate the pump (TŢ) :

Example 4.9 

A pump having a 95% volumetric efficiency delivers 25 Lpm of oil at 1200 rpm. What is the volumetric displacement of the pump?

Given Data: 

ηvol = 95%; QA = 25 Lpm = 25 × 10-3 m3/min; N = 1200 rpm.

Solution: We know that,

We also know that the theoretical discharge,

Example 4.10 

How much hydraulic power would a pump produce when operating at 125 bars and delivering 1.25 Lps of oil? What power-rated electric motor would be selected to drive this pump if its overall efficiency is 88% ? 

Given Data : 

P = 125 bars = 125 × 105 N/m2; QA = 1.25 Lps = 1.25 × 10-3 m3/s; η0 = 88% 

Solution: We know that the actual power delivered to a pump from a prime mover is called 'brake power' and the actual power delivered by a pump to the fluid is called 'hydraulic power'.

(a) To find hydraulic power :

(b) To find motor power required :

From equation (1),