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26 days ago

9

As shown, a load of mass 10 kg is situated on a piston of diameter D1 = 140 mm. The piston rides on a reservoir of oil of depth

h1 = 42 mm and specific gravity S = 0.8. The reservoir is connected to a round tube of diameter D2 = 5 mm and oil rises in the tube to height h2. Find h2. Assume the oil in the tube is open to atmosphere and neglect the mass of the piston.

1 answer:

mote1985 [204]26 days ago

7 0

Answer:

165 mm

Explanation:

The weight on the piston generates pressure on the oil using the equation:

p = f / A

Here, the force is represented by the mass's weight:

f = m * a

Where 'a' refers to the acceleration due to gravity.

A signifies the piston area, determined by:

A = π/4 * D1^2

Consequently, we have:

p = m * a / (π/4 * D1^2)

The height to which the oil will rise corresponds to that of a column that can exert equivalent pressure at its bottom:

p = f / A

The column's weight is given by:

f = m * a

The mass of this column is derived from its volume and specific gravity:

m = V * S

The volume can be calculated as the base area times the height:

V = A * h

Therefore:

p = A * h * S * a / A

We can simplify by eliminating the areas:

p = h * S * a

Next, we set pressures from both the piston and the column equal:

m * a / (π/4 * D1^2) = h * S * a

By simplifying further, we get:

m / (π/4 * D1^2) = h * S

Rearranging gives us:

h = m / (π/4 * D1^2 * S)

Here, 'h' denotes the height relative to the interface between the oil and the piston, with h1 being 42 mm. Therefore, the total height is expressed as:

h2 = h + h1

h2 = h1 + m / (π/4 * D1^2 * S)

h2 = 0.042 + 10 / (π/4 * 0.14^2 * 0.8) = 0.165 m = 165 mm

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