Hydraulics and Pneumatics: Unit 1 Review Assignment 2

MET230: Hydraulics and Pneumatics
Unit 1 Review Assignment 2
Question 1
Which of the following statements is NOT true about dynamic pumps? (Gan, 2013)
a. Centrifugal and axial pumps are classified as dynamic pumps
b. Dynamic pumps are used for low-pressure, high volume applications
c. Dynamic pumps are self-priming
d. The flow rate output of dynamic pumps decreases as the circuit resistance increases
e. None of the above
Question 2
Which of the following statements is NOT true about positive displacement pumps? (Singer
& Elliot, 2015).
a. They must be protected against overpressure by a pressure relief valve
b. The output flow rate is constant and independent of the system pressure
c. Gear, vane, and piston pumps do all belong to this category of pumps
d. Their motion cannot be reciprocating
e. None of the above
Problem 1
What is the theoretical flow rate from a fixed displacement axial piston pump with a nine-bore
cylinder operating at 1500 rpm? Each bore has a 0.75-in diameter and the stroke of 0.5 in.
Solution
 D = 0.75 m
 L = 0.5 m
 N = 1500 rpm
 K = 9
Theoretical Flow rate
Qth = π/4 . D2L . N/60 . K (Guan et al., 2014)
Qth = π/4 * 0.752 * 0.5 * 1500/60 * 9
Qth = 0.785398 * 0.5625* 0.5* 25*9
=49.70096719
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=49.70 m3
Problem 2
A vane pump is to have a volumetric displacement of 10 in3. It has a rotor diameter of 2 1
2 in, a
cam ring diameter of 3 1
2 in, and a vane width of 2.5 in. what must be the eccentricity?
Solution
To determine the eccentricity, we will follow the below process
VD = π
4 ( D c+ Dr ) eL (Wu, Y., & Lithwick, 2013).
WHERE e= eccentricity
DC = Diameter of cam ring
DR = DIAMETER OF ROTOR
L= width of the vane
Vd= volumetric displacement
Rearranging the equation, we find
e = 2 Vd
π (Dc+ Dr) L but DC= 3.5 , DR = 2.5m,
e = 2(10)
π ( 3.5+2.5 ) 2.5
= 20 / π ( 6 ) 2.5
= 20 / π (15)
= 0.4244131
= 0.4244 m
Problem 3
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Find the offset angle for an axial pump that delivers 20 gpm at 2500 rpm. The volumetric
efficiency is 95%. The pump has a nine 5
8 in diameter pistons arranged on a 5-in piston circle
diameter
Solution
In order to get the offset angle, we will follow the below procedure
The theoretical flow rate Qtr. of axial pump is obtained by
Qt = DANY tan θ......................... [1] (Hammer & Lombardo, 2011)
Where D= THE CIRCLE diameter of the piston
A = area of piston
N = the speed of the pump
Y = the number of the pistons
Θ = offset angle
The area of the cylinder thus will be
= π
4 (0.625)2
= 0.306796 m2
Substituting back 0.306796 m2 in the equation, we obtain
Qt = DANY tan θ
= 5 (0.306796 m2) (2500) (9) tan θ
= 34524.55 tan θ
Substituting back
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Qa = nvQt
0.95 * 34524.55 tan θ = 20
tan θ = 0.06
hence , θ = 3.45 degrees
Problem 4
A gear pump has a 82.6-mm outside diameter, a 57.2-mm inside diameter, and a 25.4-mm
width. If the actual pump flow rate at 2400 rpm and rated pressure is 0.002 m3/s. What is the
volumetric efficiency?
Solution
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