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Question

5.2 the following data refers to a single-acting hydraulic press. Plunger diameter: 93mm Plunger stroke: 154mm Ram diameter: 400mm Slip: 1% Calculate the following: 5.2.1. the actual volume of liquid delivered to the ram per stroke 5.2.2. the distance moved by the ram after 10 pumping strokes of the plunger 5.3. the force on the plunger of a water pump is 35kN and the work done during a delivery stroke is 7.2kJ. the diameter of the plunger is 270mm. Calculate the ffg: 5.3.1. the stroke length of the plunger 5.3.2. the pressure during a delivery stroke 5.3.3. the volume of water displaced during a delivery stroke 5.4. the diameter of the ram of an accumulator is 450mm and the mass is 13 tonnes Calculate the ffg: 5.4.1. the pressure in the fluid 5.4.2. the energy stored if the ram is lifted by 3 meters

Answer 1

(5.2.1)

Plunger Diameter = 93 mm

Radius of the 93/2 = 46.5 mm = 0.0465 m.

Diameter of the Ram = 400 mm.

Radius of the Ram = 400 / 2 = 200 mm = 0.2 m.

Stroke Length = 154 mm = 0.154 m

Slip percentage = 1%

Area of the Plunger = πr² = π(0.0465)² = 6.7929 * 10^-3 m²

Area of the Ram = πr² = π(0.2)² = 0.1256 m²

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

Volume of the Plunger per stroke = 6.7929 * 10^-3 * 0.154

Volume of the Plunger per stroke = 1.0461 * 10^-3 m³.

Volume of the Ram per stroke = Volume of the Plunger * ((100 - 1) / 100)

Volume of the Ram per stroke = 1.0461 * 10^-3 * 0.99

Volume of the Ram per stroke = 1.0356 * 10^-3 m³.

Answer 2

(5.2.2)

Plunger Diameter = 93 mm

Radius of the 93/2 = 46.5 mm = 0.0465 m.

Diameter of the Ram = 400 mm.

Radius of the Ram = 400 / 2 = 200 mm = 0.2 m.

Stroke Length = 154 mm = 0.154 m

Slip percentage = 1%

Area of the Plunger = πr² = π(0.0465)² = 6.7929 * 10^-3 m²

Area of the Ram = πr² = π(0.2)² = 0.1256 m²

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

Volume of the Plunger per stroke = 6.7929 * 10^-3 * 0.154

Volume of the Plunger per stroke = 1.0461 * 10^-3 m³.

Volume of the Ram per stroke = Volume of the Plunger * ((100 - 1) / 100)

Volume of the Ram per stroke = 1.0461 * 10^-3 * 0.99

Volume of the Ram per stroke = 1.0356 * 10^-3 m³.

Volume of the Ram for 10 pumping stroke = 1.0356 * 10^-3 * 10

Volume of the Ram for 10 pumping stroke = 0.010356 m³.

We know that Volume of the Ram = Area of the Ram * Distance travelled by ram

Therefore

Let x be the distance travelled by the ram.

Area of the Ram * Distance travelled by ram = 0.010356 m³

0.1256 * x = 0.01035

x = 0.0824 m.

Therefore distance moved by 10 pumping strokes = 0.0824 m.

Answer 3

(5.4.1)

Diameter of the Accumulator = 450 mm.

Radius of the Ram = (450/2) = 225 mm =0.225 m.

Mass of the load = 13 tonnes = 13000 kg.

Force applied on the accumulator = mg

Force applied on the accumulator = 13000 * 9.8

Force applied on the accumulator = 127400 N

Area of the Ram = πr²

A = π(0.225)r²

A = 0.1590 m².

Pressure on the Ram = Force / Area

Pressure on the Ram = 127400 / 0.1590

Pressure on the Ram = 801040 Pa

Pressure on the Ram = 801.04 kPa.

Therefore Pressure on the Fluid is 801.04 kPa.

Answer 4

(5.4.2)

Diameter of the Accumulator = 450 mm.

Radius of the Ram = (450/2) = 225 mm =0.225 m.

Mass of the load = 13 tonnes = 13000 kg.

Distance travelled by ram = 3 mt.

Force applied on the accumulator = mg

Force applied on the accumulator = 13000 * 9.8

Force applied on the accumulator = 127400 N

Area of the Ram = πr²

A = π(0.225)r²

A = 0.1590 m².

Pressure on the Ram = Force / Area

Pressure on the Ram = 127400 / 0.1590

Pressure on the Ram = 801040 Pa

Pressure on the Ram = 801.04 kPa.

Therefore Pressure on the Fluid is 801.04 kPa.

Volume of the Ram = Area of the ram * Distance moved by the ram

Volume of the Ram = 0.1590 * 3

Volume of the Ram = 0.477 m³.

Energy Stored by the ram = Pressure * Volume

Energy Stored by the ram = 801040 * 0.477

Energy Stored by the ram = 382096.08 Joules

Energy Stored by the ram = 382.096 kJ.

The Energy stored is 382.096 kJ.

Answer 5

(5.3.1)

Force on the Plunger = 35kN.

Work done during delivering stroke = 7.2 kJ.

Diameter of the Plunger = 270 mm.

Radius of the plunger = (270/2) = 135 mm = 0.135 mm.

Area of the Plunger = πr² = π(0.135)²

a = 0.05725 m²

Pressure on the Plunger = Force / Area

Pressure on the Plunger = 35000 / 0.05725

Pressure on the Plunger = 611294.7 Pa

Pressure on the Plunger = 611.294 kPa

Work done during delivering a stroke = Pressure * Volume

Volume = Work done during delivery stroke / Pressure

Volume = 7200 / 611294.7

Volume = 0.01178 m³

Volume of the Liquid Displaced = Area of the Plunger * Stroke length.

Stroke length = (Volume of the Liquid Displaced) / Area of the Plunger

Stroke length = 0.01178 / 0.05725

Stroke length = 0.205 m

Stroke length = 205 mm

Therefore the stroke length is 205 mm.

Answer 6

(5.3.2)

Force on the Plunger = 35kN.

Work done during delivering stroke = 7.2 kJ.

Diameter of the Plunger = 270 mm.

Radius of the plunger = (270/2) = 135 mm = 0.135 mm.

Area of the Plunger = πr² = π(0.135)²

a = 0.05725 m²

Pressure on the Plunger = Force / Area

Pressure on the Plunger = 35000 / 0.05725

Pressure on the Plunger = 611294.7 Pa

Pressure on the Plunger = 611.294 kPa

We know that Pressure on Plunger = Pressure on the Ram

Pressure on the Ram = 611.294 kPa

Therefore the pressure during delivery stroke is 611.294 kPa.

Answer 7

(5.3.3)

Force on the Plunger = 35kN.

Work done during delivering stroke = 7.2 kJ.

Diameter of the Plunger = 270 mm.

Radius of the plunger = (270/2) = 135 mm = 0.135 mm.

Area of the Plunger = πr² = π(0.135)²

a = 0.05725 m²

Pressure on the Plunger = Force / Area

Pressure on the Plunger = 35000 / 0.05725

Pressure on the Plunger = 611294.7 Pa

Pressure on the Plunger = 611.294 kPa

Work done during delivering a stroke = Pressure * Volume

Volume = Work done during delivery stroke / Pressure

Volume = 7200 / 611294.7

Volume = 0.01178 m³

We know that Volume of the Plunger = Volume of the Ram when no slip is present

Volume of the Liquid displaced during delivery stroke = 0.01178 m³.