Hydraulic circuits

Explain what hydraulics is and what fluid it uses, and name two machines that operate with it, stating what job each one performs.

State Pascal's principle in your own words and explain it using the example of a water-filled syringe with the outlet blocked: what happens to the pressure at any point in the liquid when the piston is pushed.

A piston exerts a force of $300\ \text{N}$ on a surface area of $0{,}01\ \text{m}^2$. Applying $p = \frac{F}{S}$, calculate the pressure sustained by the oil, expressed in pascals.

The figure shows a hydraulic press with its data: a force on the small piston and both surface areas. Calculate the circuit pressure and the force $F_2$ pushing the large piston, and explain why the force is multiplied.

In a hydraulic press, the small piston has a surface area $S_1 = 10\ \text{cm}^2$ and the large one, $S_2 = 100\ \text{cm}^2$. If a force $F_1 = 50\ \text{N}$ is applied, calculate the oil pressure and the force $F_2$ pushing the large piston, and explain how many times the force has been multiplied.

A hydraulic jack has pistons of $5\ \text{cm}^2$ and $50\ \text{cm}^2$ and must lift a load of $1.000\ \text{N}$. Calculate what pressure the oil needs and what force must be applied to the small piston. (Given: $10\ \text{N}/\text{cm}^2$ is equivalent to $1\ \text{bar}$.)

Make a comparison table between pneumatics and hydraulics with the following rows: fluid used, typical working pressure (about $6\ \text{bar}$ compared to over $100\ \text{bar}$), force it can provide, effect of a leak, and a typical application.

A car brake is hydraulic. Describe the path followed by the pressure from the pedal to the wheel brake calipers, and explain why it would not be a good idea to make it pneumatic, considering the compressibility of air and precision.

The figure shows a hydraulic circuit with its symbols: reservoir, pump, a valve, and a double-acting cylinder, with a component marked with ?. State what component it is, what function it performs, and what happens to the rod when moving the lever in one direction and in the other.

A student in the workshop claims: "In a hydraulic press with pistons of $5\ \text{cm}^2$ and $100\ \text{cm}^2$, if I apply $40\ \text{N}$ on the small piston, I get $800\ \text{N}$ on the large one. Since the force is multiplied by 20, we've created free energy!".\n\na) Calculate the pressure sustained by the oil and show how much the large piston rises when the small piston moves down $10\ \text{cm}$, reasoning from the displaced fluid volume.\nb) Calculate the mechanical work done at the input ($W_1 = F_1 \cdot \Delta x_1$) and at the output ($W_2 = F_2 \cdot \Delta x_2$).\nc) In light of your calculations, refute the student's claim: justify which quantities are multiplied, which are divided, and what fundamental physical principle prevents the "free creation" of energy in a hydraulic machine.

The figure shows a hydraulic jack with its data. Calculate the force $F_2$ that lifts the load and the oil pressure, and work out how many pump strokes are needed for the load to rise $2\ \text{cm}$ if in each stroke the small piston moves down $4\ \text{cm}$.

During the brake test of a vehicle after an intervention in the workshop, the driver notices that the pedal sinks almost to the floor with a "spongy" feel and the brake calipers barely exert any force on the discs. After inspecting the pipes, it is confirmed that there are no external fluid leaks.\n\na) Interpret this failure at a physical level: compare the behavior of a liquid and a gas under pressure. Why does the presence of an air bubble prevent the effective application of Pascal's principle in the circuit?\nb) Analyze what happens to the mechanical work exerted by the driver's foot during the pedal's dead travel: where is that energy spent if it does not reach the brakes?\nc) Explain the technical bleeding procedure required to fix the fault and justify why no manufacturer designs passenger car brake systems that use compressed air instead of hydraulic fluid.

You have to design a compact hydraulic press to press-fit bearings, capable of reaching a pressing force of at least $5.000\ \text{N}$ by applying a manual effort of $250\ \text{N}$ at most.\n\na) Demonstrate from Pascal's principle what relationship must exist between the radius of the large piston ($r_2$) and that of the small piston ($r_1$). Justify mathematically why doubling the radius of a piston multiplies the force by four and not by two.\nb) A manufacturer supplies commercial cylindrical pistons with standardized radii in whole centimeters ($r = 1\ \text{cm},\ 2\ \text{cm},\ 3\ \text{cm},\ \dots,\ 10\ \text{cm}$). If, due to space limitations, the large piston cannot have a radius greater than $7\ \text{cm}$, select the optimal commercial pair $(r_1, r_2)$ to achieve the goal and calculate the exact real force it will deliver.\nc) If the small piston of your design advances $6\ \text{cm}$ in each stroke, calculate how much the large piston will advance. What practical consequence does this stroke have on the total operating time of the press?