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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Pressure

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Bernoulli's Equation
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Pressure in Fluids for A-Levels
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:pressure/4030/


Example 1.

A liquid sprayer is taken - see picture. The sprayer creates a vacuum by means of an airflow created by squeezing a rubber pump. The undercoat lifts the liquid from the container, pushes it into a horizontal tube, and disperses it - see picture. What must be the minimum velocity of the airflow to raise the liquid by 6 cm? The density of the liquid is and of the air is . The pressure above the liquid in the tank is equal to the normal air pressure.


Liquid sprayer

    
Example 2.

A jet is flying just above the water as shown in the figure. Behind it rises pillars of water of height of 8 m as shown in the figure. Estimate the velocity of the exhaust gas of both engines. The density of the exhaust gas is and that of the water is .


Jet over water

    
3.

The water reaches a height of 1 m in a wide container. A small hole is drilled at a height of 30 cm above the bottom of the container through which a stream of water flows. At what height should we drill the second hole so that the water flowing from the two holes hits the ground at the same horizontal distance from the container?

    
4.

We want to measure the speed of a river flow at a certain depth. For this purpose, we use a rectangular tube that has a horizontal strip at a depth where we want to measure the flow, and the opening is directed towards the flow. The vertical strip is out of the water. The tube is open on both sides. It's called the Pitot tube. The water in the pipe rises by 20 cm. What is the speed of the river flow?

    
5.

An example of the application of Bernoulli's equation is the Venturi tube. It is used to measure the velocity of a liquid in pipes. The tube is slightly tapered on a short section (see figure). As a result, the pressure in this part is slightly less than the pressure in the wider part of the pipe. With the help of a mercury manometer, we can measure the pressure difference between the two parts of the pipe and calculate the flow velocity.


The heights of the mercury manometer columns (see figure) differ by 7.5 cm. What is the velocity of the water in the pipe? The cross-sectional areas of the pipe are and the density of mercury is and that of water is .


Venturi tube

    
6.

A wide water-filled container has a small opening close to its bottom. The cross-sectional area of the container is much larger than the cross-sectional area of the opening. The height of the water from the surface to the opening is 60 cm. At what speed does water flow through the opening? The viscosity is neglected and the water density is .

    
7.

A pot and bottle have the same volume and are filled with water. Write down which vessel has the highest pressure at the bottom of the vessel.


Pot (left) and bottle (right)

    
8.

A hydraulic press has a smaller piston with an area of and a larger piston with an area of . A force of is applied on the smaller piston. With what force does the larger piston act?

    

9.

There is water in a round reservoir with an open top. The water pressure is measured with a mercury manometer connected to the reservoir as shown in the figure below. On the left arm of the manometer, the mercury level is lower than the centre of the sphere. The right arm of the manometer is open at the top and the mercury level is higher than on the left arm. What is the radius of the reservoir?


The density of mercury is and the density of water is .


Round reservoir with water and mercury manometer

    
10.

On which quantities does hydrostatic pressure depend?


  • Depth,

  • Bottom surface,

  • Container shape,

  • Fluid density.

    
11.

A fish swims in an aquarium with length 35 cm, width 17 cm, and depth 27 cm, filled with water to the top. Calculate in Pa and kPa, the change in pressure on the fish when it drops from the surface to the bottom of the aquarium.

    
12.

We know that water pressure increases with depth.

  • What pressure change does a diver feel in Lake Windermere when he dives from the surface to the depth of 31 m?

  • What is the actual pressure felt by the diver? Note that the air pressure on that day is equal to 103 kPa.

    
13.

Casey wants to drink water from the bottom of a 5 cm deep glass using a straw. How much vacuum does she have to create with her mouth if the straw is 19 cm long and reaches the bottom of the glass?

    
14.

A large plate is dropped into a lake. It has a built-in measuring sensor for measuring the force on the entire plate. The plate rests at a depth of . What force is detected by the measuring sensor, taking into account that the air pressure at the depth is ?

    
15.

In a small barrel filled with liquid, a 26 m long vertical pipe is led to the bottom of the barrel. When the pipe is filled to the top with the same liquid, the barrel explodes at a pressure of 260 kPa. Use the pipe to determine which liquid is in the barrel. Disregard the air pressure in the pipe.


Bashed pipe

    
16.

How many kPa pressure is measured 117 m below sea level? The air pressure is 101 kPa and density of sea water is .

    
17.

A bottle has a bottom area of and a height of . What is the pressure at the bottom of the bottle if it is filled to the top with oil and closed with a stopper? Specific weight of oil is .

    
18.

A vertical glass tube contains oil with a density of poured to a height of . In another tube, however, we have water. How high must the water reach if we want the pressure at the bottom of both tubes to be the same?


    

19.

What force does the air pressure have on each square decimeter of a surface? Air pressure is .

    
20.

By how much is the pressure at the bottom of a 3 dm tall mercury-filled vessel greater than the pressure at the surface? The specific weight of mercury is .

    
21.

The brake pedal of a car is pressed with a force of 30 N. The lever (a = 20 cm, b = 4cm) - see the figure below - transmits the force to the smaller piston of the brake oil pipe. The larger piston on the other side of the pipe applies force on the brake linings. What is this force?


The areas of the smaller and larger pistons are given as and respectively.


Hydraulic brake

    
22.

How high must the column of mercury be to have the same pressure as 5 m below the lake level? The specific weights of mercury and water are and respectively. Round the result to the nearest centimeter.

    
23.

A wooden block weighing lies on an inflatable cushion and covers an area of . The area of the inflatable cushion opening is one-thousandth that of the flat area covered by the square. How much force do we have to exert on the opening so that air does not escape from the cushion?

    
24.

A crate with a mass of is to be lifted with a hydraulic lift. The piston under the crate has an area , and on the other side is the piston with the area . With at least as much force, you have to press on the smaller piston to lift the crate. How much force is needed? Round the result to one decimal place.


Hydraulic lift

    
25.

Water is poured in a deep glass with an opening of cross-sectional area . We then place a light plate on it and turn it over.

  • Why doesn't the water run out of the glass?

  • What is the mass of the load needed to be hung on the plate to make the water run out?


    Density of water is , air pressure is and gravitational acceleration is .

    
26.

How much does the air pressure drop when we climb to the top of a high skyscraper? The density of air at the ground is . Assume that at this height difference, the air density does not change significantly.

    
27.

Two syringes are connected by a hose and filled with water. The larger syringe has a piston with an area , and the smaller syringe has a piston with an area . The piston of the larger syringe is pressed with a force of . What is the least force with which we have to press the piston of the smaller syringe to move the piston of the larger syringe? Round the result to one decimal place.


Syringes connected to a hose and filled with water

    
28.

Mercury is poured into a curved tube and of an unknown liquid is added to the right arm. This creates a difference in the height of mercury between the left and right arm. What is the density of the unknown liquid?


The density of mercury is .

    

29.

There is water up to a height of 10 cm in a closed container, and compressed gas is above the water. A manometer is connected to the container as shown in the figure below. The manometer tube is open at the top. The water reaches a height of 60 cm in the manometer tube. What is the pressure of the gas in the container? The air pressure is 1 bar, and the density of water is .


Closed container with water, gas and manometer

    
30.

A diver produces air bubbles during exhalation while diving to a depth of 12 meters. What is the air pressure in these bubbles?


Note that:


    
31.

A large homogeneous ball of aluminum of radius 0.5 m is thrown into a deep lake and the ball slowly sinks to the bottom of the lake. By how much does the volume of the ball change when it is at a depth ? The compressibility of aluminum is .

    
32.

A cube-shaped pool is filled with water at a constant inflow of 20 litres per second. The bottom of the pool with an area of can withstand a pressure of .

  • How high can the water reach before the bottom of the pool pulls out?

  • What is the pressure at the bottom of the pool after 1 hour?

  • What is the pressure at half the height of the water after 2.5 hours?

    
33.

Two solid cylindrical objects X and Y are held fully submerged in a liquid, as shown.




The objects have the same volume. The density of the material of Y is twice the density of the material of X. Both objects are stationary. Which statement is correct?


  • The pressure difference due to the liquid between the top and bottom surfaces of X is the same as that for Y.


  • The weight of X is the same as the weight of Y.


  • The force due to the liquid acting on the top surface of X is greater than that acting on the top surface of Y.


  • The upthrust acting on X is the same as the upthrust acting on Y.

    
34.

Which expression for pressure is correct?


  • mass per unit area


  • force per unit area


  • weight per unit volume


  • mass per unit volume


    
35.

One end of a U-shaped tube is attached to a gas tap, with its other end open to the atmosphere. It contains water of density and the heights of both sides of the water column are shown.




The atmospheric pressure is . What is the pressure of the gas from the gas tap?









    
36.

A U-shaped glass tube contains liquid of density , as shown.




What is the difference in pressure due to the liquid between levels P and Q?









    
37.

A solid wooden cube rests on a horizontal surface. What gives the pressure exerted by the weight of the cube on the horizontal surface?


  • the product of the acceleration of free fall, the density and the side length of the cube


  • the product of the acceleration of free fall, the density and the volume of the cube


  • the product of the acceleration of free fall, the density and the area of one face of the cube


  • the product of the acceleration of free fall and the density of the cube


    
38.

Water of depth is covered by oil of depth in a measuring cylinder. The density of the water is and the density of the oil is . What is the total pressure exerted on the base of the measuring cylinder due to the oil and water?









    

39.

Atmospheric pressure at sea level has a value of . The density of sea water is . At what depth in the sea would the total pressure be ?









    
40.

A submarine carries a pressure meter so that the crew can work out how far they are below the surface of the sea. At the surface, the meter indicates a pressure of . The density of seawater is . What is the depth below the surface when the meter reads ?









    
41.

A child drinks a liquid of density through a vertical straw. Atmospheric pressure is and the child is capable of lowering the pressure at the top of the straw by 10%. The acceleration of free fall is . What is the maximum length of straw that would enable the child to drink the liquid?









    
42.

The density of mercury is . The pressure difference between the bottom and the top of a column of mercury is . What is the height of the column?









    
43.

The graph shows how the pressure exerted by a liquid varies with depth below the surface. What is the density of the liquid?











    
44.

The diagram shows two liquids, labelled P and Q, which do not mix. The liquids are in equilibrium in an open U tube. What is the ratio ?











    
45.

A cylindrical block of wood has a cross-sectional area and weight . It is totally immersed in water with its axis vertical. The block experiences pressures and at its top and bottom surfaces respectively. Which of the following expressions is equal to the upthrust on the block?









    
46.

At a depth of in a liquid of density , the pressure due to the liquid is . Another liquid has a density of . What is the pressure due to this liquid at a depth of ?