force number of strokes

Question

5.2 The following data refers to a single acting hydraulic jack: Diameter of the ram = 510 mm Diameter of the plunger = 15% diameter of the ram Plunger stroke length = 100 mm Mechanical advantage on the lever = 25 Calculate the following: 5.2.1 The force to be applied to the lever to lift a load of 5 tons if the slip is 9% (4) 5.2.2 The number of pumping strokes needed to lift a load 410 mm if there is no slip

Answer 1

(5.2.1)

The diameter of the ram = 510 mm.

Diameter of the plunger = 15% of the diameter of the ram

Diameter of the plunger = (15/100) * 510 mm = 76.5 mm

Mechanical advantage on the lever = 25

length of load arm / length of effort arm = 25

l1 / l2 = 25

Mass of the load = 5 tonnes

Mass m = 5 * 1000 = 5000 kg.

Force = mg

F = 5000*9.8 = 49000 N.

Force applied to lift the load = 49000 * 25

F1 = 1225 kN.

Force applied to the lever to lift the load = 1225 kN.

Answer 2

(5.2.2)

The diameter of the Ram = 510 mm.

Diameter of the Plunger = 15% of the diameter of the ram

Diameter of the Plunger = (15/100) * 510 mm = 76.5 mm

Stroke length of the Plunger = 100 mm = 0.1 m

Distance travelled by the laod = 410 mm = 0.41 m

Radius of the Ram = 510 / 2 = 255 mm = 0.255 m

Radius of the Plunger = 76.5 / 2 = 38.25 mm = 0.03825 mm

Area of the Ram = πr² = π(0.255)²

Area of the Ram = 0.2042 m²

Area of the Plunger = πr² = π(0.03825)² = 4.596 * 10^-3

Number of pumping strokes = (Total volume of the liquid displacement) / (Volume of the liquid per stroke)

Total volume of the liquid displacement = Area of the ram * Distance travelled by the weight.

Total volume of the liquid displacement = 0.2042 * 0.41

T = 0.0837 m³

Volume of the liquid per stroke = Area of the plunger * Stroke length

Volume of the liquid per stroke = 4.596 * 10^-3 * 0.1

Volume of the liquid per stroke = 4.596 * 10^-4

Number of pumping strokes = (0.0837) / (4.596 * 10^-4)

n = 182.11 strokes.

Number of pumping strokes = 182.11.