Understanding Hydraulic System Overview

Understanding Hydraulic System 01

Understanding Hydraulic System + Lever 02

Barometer with a layer of water – Find height of mercury H

Answer: Option B

Man Jumps Vertically Upwards, Pressure On Ground Is Greater During The Jump

This concept is similar to a 2016 O-Level Pure Physics Question P2 Q2, on why the pressure acting on the ground is greater during the jump, compared to when he is standing stationary on the ground.

During the jump, his leg will exert an upward force. This upward force (equivalent to normal force or force on the man by the ground) is greater than the weight of the man. Hence there is a net (resultant force) upwards, causing him to accelerate upwards.

That force on the man by the ground is equal and opposite to the force on the ground by the man. This is an action-reaction pair. Since the force exerted on the ground by the man is greater (greater than weight), the pressure exerted on the floor is greater.

(NOTE: Normal force and Weight is not an action-reaction pair)

Liquid Pressure Summary Part 2

Another P1V1 = P2V2 question

Solution: Option C

When to use the concept PV = constant and P1V1 = P2V2 to solve?

When temperature is constant (for o-level), when a fixed mass of gas (fixed number of air molecules) is compressed in a closed system (e.g. piston), the volume V decreases and pressure P increases, and vice versa.

But when you multiply pressure and volume, PV, it is always a constant.

PV = constant

Hence we can always equate the PV of the first scenario = to the PV of the second scenario, provided there is no addition or removal of air molecules from the system.

Hence, you have P1V1 = P2V2

The followings are 4 different questions which require this concept to solve. Do revise them.

Solutions: Option D (refer to the worked solutions below)

Solutions: Option D

Solutions: A

4)

Solutions:

 

5) 

Solution: Option C

Examples of a hydraulic system

Boiling water at 60 °C in lab!

Water boils at 100°C. In the view below, the water is initially at around 60°C.

How is this possible?

Explanation:

At sea level, where the pressure is atmospheric pressure (approx 105 000 Pa), the boiling point of water is 100°C.

In the video as air is sucked from the sealed container, the pressure in the container decreases. This lowers the boiling point of the water to around 60°C, hence water will boil and bubbles are formed.

It is similar to boiling water at high altitude, like on top of Mount Everest (about 8 km high). Water will boil around 70°C to to lower atmospheric pressure at high altitude.

Physics of Construction Lifting Truck

1) Why are the 4 extended legs necessary?
This is to increase the area of base of the truck to increase the stability. From our theory, as long as the weight acting vertically downward from the centre of gravity is within the area of base, there will be a restoring moment to bring the truck back to its original position, hence increases its stability.

2) In what situation will the truck topple? (note the the centre of gravity (CG) of the truck is in general very low due to mass concentration at the base)
Basically, there are 2 situdation:
– if the load that is lifted is too heavy, the overall new CG of the truck and load might shift outside the area of base, hence causing the truck to topple. i.e. the clockwise moment created by the load is created than the anticlockwise moment created the weight of truck.
– If the angle of tilt is too much which increases the perpendicular distance from load to pivot. Likewise, the overall CG might be outside the area of base and there is a net clockwise moment.

3) What is the purpose of the metal plate underneath the legs?
The purpose is to increase the area of base. The whole weight of the truck is spread over the 4 legs. Since P = F/A, with a bigger base area, the pressure acting on the ground will be reduced. This is to minimise any damages done to the ground.

N2004 P1 Q15 – Pressure P1V1 = P2V2

Water if depth 10 m exerts a pressure equal to atmospheric pressure. An air bubble rises to the surface of a lake which is 20 m deep. When the bubble reaches the surface, its volume is 6 cm³.

 

 What was the volume of the air bubble at the bottom of the lake?

 

A) 2 cm³          B) 3 cm³         C) 12 cm³      D) 18 cm³

 

 

Solutions: Option A

Since the air bubble is enclosed, PV at A is equal to PV at B.

                  P_AV_A = P_BV_B

(P_atm + P_water) V_A = (P_atm) V_B

        (10 + 20) V_A = 10 x 6

                      V_A = 60 / 30

                           = 2 cm³

 

Using barometer to estimate height of mountain

At sea-level, the barometer which Pie is holding reads 760 mm of Hg. When he is at the top of Mount Pie, the same barometer reads 230 mm of Hg.
Given take the density of mercury to be 13.6 g cm^-3 and the density of air, 1.23 x 10^-3 g cm^-3.

Estimate the height of the mountain?

Solutions: 5860 m

Pressure difference in mercury, Pmercury = pgh

= 13600 x 10 x (0.76 – 0.23)

= 72080 Pa

Pressure difference, Pair = pgh

               72080 = 1.23 x 10 x h

                     h  = 5860 m

In general, barometer can be used to estimate altitude. As height increases, height of mercury column will decreases. Such measurement is just an estimation as the density of air varies with various altitudes. Density of air is lower higher up in the mountain as the air is thinner.
In addition, It is not practical to bring around a mercury barometer as mercury is a heavy liquid and is poisonous.

An aneroid barometer (no mercury inside though) is used to measure altitude more accurately.

Pressure – Manometer and how mercury levels in both limbs move as pressure changes

The diagram shows a manometer connected to a gas cylinder of large volume. The atmospheric pressure is 76 cm Hg.

Due to the pressure of the gas cylinder, the mercury level in the left limb is at 30 cm while the mercury level in the right limb is at 0 cm.

Actually there is a short-cut. If atmospheric pressure remains constant, when the pressure of the gas cylinder decreases by 20 cm Hg, the difference in mercury levels between the left and right limbs decreases from 30 cm Hg to 10 cm Hg.

If you understand this, straight away you will be able to tell that the mercury height difference between left limb and right limb is 10 cm Hg.

You can then consider the markings on the manometer.  When the drop in pressure is 20 cm Hg, note that mercury level on one limb will increase by 10 cm and the other limb will decrease by 10 cm. Shared equally!

Liquid Pressure Video

Liquid pressure, P = ρgh.

ρ is the density of the liquid (kg/m³) ,
g is the gravitational field strength (10 N/kg), and
h is the vertical height from the surface of the liquid (m)

In this video, since the last outlet is the lowest (greatest height from the liquid surface), the pressure is the greatest. Hence water ejects out with the greatest force and longest distance.

<p><a href=”https://vimeo.com/24961365″>Liquid Pressure</a> from <a href=”https://vimeo.com/user7367248″>evantoh</a&gt; on <a href=”https://vimeo.com”>Vimeo</a&gt;.</p>

Water finds its own level

<p>Water finds its own level from evantoh on Vimeo.</p>

Hydraulic System – Basic Concepts

Hydraulic System is a useful system which allows you to lift heavy load by just applying a small force.

Liquid is used (over gas) in hydraulic system as liquid is incompressible.

Enclosed liquid is able to transmit pressure to all parts of the system. In other words, pressure throughout the system is constant.

View the video tutorial for the concept of hydraulic system and Conservation of Energy.

Hydraulic System

A common question on P=F/A but students always get confused.

Take note of all units. To find the pressure in Pa, the units for F must be N and the area must be m².

For (a) and (b)

Note that pressure acting on the floor by all the 3 legs is the SAME as the pressure acting on the floor by each of the leg.

In this case, the total weight of Pie and the stool is spread over 4 legs.

F = weight = 65 x 10 = 650 N

A = 25 cm² = 25 ÷ 100² = 0.0025 m²

P = F/A = 650 / (0.0025 x 4) m² = 65 000 Pa = 65 kPa

For (c)

When there are only 3 legs, the weight (still the same) is now spread over a smaller area. Hence pressure should increase.

P = F/A = 650 / (0.0025 x 3) m² = 86666.67 Pa = 86 700 Pa = 86.7 kPa

Women = Dangerous

Basic of P = F/A – 1 foot vs 2 feet on ground

Basic formulae for Pressure

The 2 important formulae for Pressure.

It is of great importance that you take note of the units.

For P = F/A
– If finding pressure (P) in Pascal (Pa), make sure that the area is in m³,  if you use cm³, it will be wrong.

All units must be consistent.

To revise on unit conversion for density – kg/m³ to g/cm³, or vice versa, click on the post.