Math Editor

Hydraulics Formulae

Pressure formula

P= AF​

P=4πd2​F​

P=4πD2W​​

(Pascal - Pa)

Pressure at a Point

P=pgh

Density

p=vm​

Hydraulic Press Calculations

Pressure below piston = pressure below ram

AF​=AW​

4πd2F​​=4πD2W​​

d2F​=D2W​

FW​=d2D2​

Notes:

W= weight on the ram

F= force applied to the piston

Calculating the Volume of Liquid Required per Stroke by the Press (taking slip into account)

V=4πd2​×s

V=4πD2​×h

Notes:

d = piston diameter

s = stroke length of the piston

D = ram diameter

h = ram height

Calculating the Relationship between the Ram and Piston Motion

Volume liquid displaced by ram = Volume liquid displaced by piston

4πD2​×L=4πd2​×s×n

D2×L=d2×s×n

n=d2D2​×sL​

Notes:

n=number of strokes

1000l= 1m3 (all substances)

1l=1kg (only water)

Calculating the Relationship Between the Load on the Punger and Effort on the Lever

Mechanical Advantage

What is the Mechanical Advantage of a Lever System?

The Mechanical Advantage of a Lever System means that the Effective Force on the Plunger is greater than the Force (Effort) applied to the handle of the lever.

If we ignore losses to due to friction, the following formula applies:

MA=EffortonHadle(W)PlungerLoad(F)​

Efficiency Calculations

η=workinputworkoutput​×100%

η=powerinputpoweroutout​×100%

η=volumeinputvolumeoutpht​×100%

η=appliedeffortplungeractualeffortonplunger​×100%

η=appliedforceonramactualforceonram​×100%

Calculating Slip

η=100−slip

Slip=100−η

Calculating Work Done by the Press(Taking Efficiency into Account)

Workdone=F× D

=F×s

Workdone=pV

Work done=increase in potential energy

Work done =mgh

Work done=Vρgh [where Vρ=mass]

Power (P) =tpV​

Calculating the Relationship Between Plunger Movement and Ram-Piston Movement

Work Done by Plunger = Work Done on Ram

F×s=W×L

Volume of fluid displaced by plunger = Volume of fluid that displaces ram

4πd2​×s=4πD2​×L

d2×s=D2×L

Calculating the Force Exerted by RAM

1. When calculating the force exerted on the ram, first find the Force Applied on the Ram by using the following formula:

2. Secondly Calculate Actual Force on Ram by using the following formula: