Hydraulic circuits

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.

Imagine two closed syringes, one filled with air and the other filled with water. Explain what happens when pressing each piston and reason why hydraulics takes advantage of the fact that liquids are hardly compressible.

Explain, using the concept of force multiplication, why a hydraulic jack allows a car to be lifted by operating a lever with one hand.

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 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.

Match each component of a hydraulic circuit to its function: (a) pump, (b) oil reservoir, (c) hydraulic cylinder, (d) directional control valve. Functions: (1) pump the oil and pressurise it, (2) store the circuit's oil, (3) convert pressure into motion, (4) direct the oil to one side of the cylinder or the other.

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.

Explain what the pump does within a hydraulic circuit, how it differs from a compressor, and what happens to the circuit if the reservoir runs out of oil while the pump is running.

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 $1\ \text{bar}$.)

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?

A flow regulation gate is operated by a double-acting hydraulic cylinder powered by a unit providing a constant working pressure of $60\ \text{bar}$ ($600\ \text{N/cm}^2$) and a flow rate of $9\ \text{L/min}$ ($150\ \text{cm}^3/\text{s}$). The piston has a cross-sectional area of $30\ \text{cm}^2$ and the rod has a cross-sectional area of $10\ \text{cm}^2$.\n\na) Calculate the maximum theoretical force exerted by the cylinder during the advance stroke (rod extension) and during the return stroke (rod retraction). Justify why they are not equal based on the effective surface area of each chamber.\nb) Calculate the linear velocity of the rod when advancing and retracting in $\text{cm/s}$, knowing that $v = Q / S_{\text{useful}}$.\nc) Interpret the results obtained: an operator claims that the cylinder will take exactly the same time to open the gate as to close it. Prove with data whether the statement is true or false and explain the trade-off relationship between force and speed in this type of actuator.

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.

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.

On a workshop hydraulic lift with a single-acting cylinder holding a $1.600\ \text{kg}$ passenger car, the throttle and return valve is manually opened to lower it, with the electric pump switched off.\n\na) Justify physically where the energy comes from to evacuate the oil from the cylinder chamber and push it back to the reservoir without the help of a motor. What energy transformation takes place during the descent?\nb) With the return valve closed and the pump stopped, the mechanic observes that the vehicle loses height at a rate of $5\ \text{mm}$ per minute. Formulate two technical hypotheses about which component of the hydraulic circuit might be failing to cause this unintended descent.\nc) Explain why occupational risk prevention regulations prohibit working under a load supported solely by hydraulic pressure and describe what redundant, fluid-independent safety mechanism must mandatory be engaged to protect the mechanic.