Engineering Mechanics

(^464) „„„„„ A Textbook of Engineering Mechanics

6. Measuring the diagram to scale, we find
   OB = 1.45 m and OC = 1.1 m
   We know that the velocity of C,
   11 1.1
   8.3 m/s
   1.45

B

C

vOC

v

OB

× ×

=== Ans.

22.7. ANALYTICAL METHOD FOR THE VELOCITY OF PISTON OF A

RECIPROCATING PUMP

Fig. 22.11 Veloctiy of a piston of reciprocating pump.

Consider the mechanism of a reciprocating pump, in which AB be the crank, BC the connecting

rod, and C the piston. Let O be the instantaneous centre of the connecting rod BC. Produce the line

CB to meet the vertical line through A at N as shown in Fig. 22.11. Now through B, draw BM

perpendicular to CA.

From the geometry of the triangle OCB and ABN, we find that these two triangles are similar.

Therefore

OC AN

OB AB

=

Let ω 1 = Angular velocity of the crank AB in rad/s.

ω 2 = Angular velocity of the connecting rod BC about O, in rad/s.

l= Length of the connecting rod BC,

r= Radius of the crank AB,

θ= Angle traversed by the crank in degrees,

φ= Angle, which the connecting rod makes with CA (known as

obliquity of the connecting rod).

We know that velocity of piston or C,

vC=ω 2 × OC ...(i)

and velocity of B, vB=ω 2 × OB ...(ii)