how to calculate

Question

5.3 The following data refers to a single -acting hydraulic press: in - Area of plunger a = 25 % of ram area - Stroke of plunger = 0.161 m - Force applied to the plunger = 560 N 10 - Area of the ram piston = 0,524 m2 ,.., Neglect ALL the losses. Calculate the following: 5.3.1 The volume of liquid displaced by the plunger in 12 pumping strokes 5.3.2 The distance moved by the ram piston in mm after 1 pumping stroke of the plunger 5.3.3 The force exerted by the ram piston 5.3.4 The mechanical advantage of the press 5.3.5 The fluid pressure in the liquid

Answer 1

(5.3.1)

Area of Plunger = 25% of area of Ram

Stroke length of plunger = 0.161 m.

Force applied to the plunger = 560 N.

Area of the Ram piston = 0.524 m².

Area of Plunger = 25% (0.524)

Area of Plunger = 0.131 m².

Volume of the Plunger = Area of the Plunger * Stroke of Plunger.

Volume of Plunger per stroke = 0.131 * 0.161

Volume of Plunger per stroke = 0.021091 m³.

Volume of Plunger for 12 pumping stroke = 0.021091 * 12

Volume of Plunger for 12 pumping stroke = 0.253092 m³.

Therefore Volume of Plunger for 12 pumping stroke = 0.253092 m³.

Answer 2

(5.3.2)

Area of Plunger = 25% of area of Ram

Stroke length of plunger = 0.161 m.

Force applied to the plunger = 560 N.

Area of the Ram piston = 0.524 m².

Area of Plunger = 25% (0.524)

Area of Plunger = 0.131 m².

Volume of the Plunger = Area of the Plunger * Stroke of Plunger.

Volume of Plunger per stroke = 0.131 * 0.161

Volume of Plunger per stroke = 0.021091 m³.

Let x be the distance travelled by the Ram Piston.

Volume of Ram Piston = Area of the Ram * Distance travelled by Ram Piston

Volume of Ram Piston = 0.524 * x

Volume of Ram Piston = 0.524x

We know that

Volume of the Plunger = Volume of Ram Piston

0.021091 = 0.524x

x = 0.021091 / 0.524

x = 0.04025 m.

x = 40.25 mm

Distance travelled by Ram Piston = 40.25 mm.

Answer 3

(5.3.3)

Area of Plunger = 25% of area of Ram

Stroke length of plunger = 0.161 m.

Force applied to the plunger = 560 N.

Area of the Ram piston = 0.524 m².

Area of Plunger = 25% (0.524)

Area of Plunger = 0.131 m².

We know that

Pressure on Ram = Pressure on Plunger

(Force on Ram / Area of Ram) = (Force on Plunger / Area of the Plunger)

Force on Ram = (Force on Plunger / Area of the Plunger) * Area of Ram

Force on Ram = ( 560 N / 0.131) * 0.524

Force on Ram = 560 * (0.524 / 0.131)

Force on Ram = 560 * 4

Force on Ram Piston = 2240 N

Therefore Force on Ram Piston is 2.240 kN.

Answer 4

(5.3.5)

Area of Plunger = 25% of area of Ram

Stroke length of plunger = 0.161 m.

Force applied to the plunger = 560 N.

Area of the Ram piston = 0.524 m².

Area of Plunger = 25% (0.524)

Area of Plunger = 0.131 m².

Pressure on liquid = Force on the Plunger / Area of the Plunger

Pressure on liquid = 560 / 0.131

Pressure on liquid = 4274.8 Pa

Pressure on liquid = 4.274 kPa

Therefore Fluid Pressure of the Liquid = 4.274 kPa.

Answer 5

(5.3.4)

Area of Plunger = 25% of area of Ram

Stroke length of plunger = 0.161 m.

Force applied to the plunger = 560 N.

Area of the Ram piston = 0.524 m².

Area of Plunger = 25% (0.524)

Area of Plunger = 0.131 m².

We know that

Pressure on Ram = Pressure on Plunger

Pressure of the Ram = Weight of Ram/ Area of the Ram

(Weight of Ram / Area of Ram) = (Force on Plunger / Area of the Plunger)

Weight lift of Ram = (Force on Plunger / Area of the Plunger) * Area of Ram

Weight lift of Ram = ( 560 N / 0.131) * 0.524

Weight lift of Ram = 560 * (0.524 / 0.131)

Weight lift of Ram = 560 * 4

Weight lift of Ram = 2240 kg.

Weight  with respect to gravitational force g .

Weight lift of Ram = 2240*g 

Weight lift of Ram = 2240 * 9.8

Weight lift of Ram = 21952 N

Mechanical Advantage  = Weight Lift by Ram / Force applied on the Plunger

MA = 21952 / 560

MA = 39.2

Therefore Mechanical Advantage of the Hydraulic Press is 39.2.