Hydrostatics

Question 1

Hydrostatics (true or false):

Is the study of fluids in dynamic states

Answer 1

False. Hydrostatics is the study of fluids at rest.

Question 2

Hydrostatics (true or false):

Investigates compressible fluids at rest

Answer 2

False. Hydrostatics deals with incompressible fluids such as liquids.

Question 3

Hydrostatics (true or false):

Investigates incompressible fluids at rest

Answer 3

True. Hydrostatics deals with incompressible fluids such as liquids.

Question 4

Hydrostatics (true or false):

Is time-sensitive

Answer 4

False. Given an expanded timescale, ice and even rock can be considered fluids, but in their ‘solid’ state these are not relevant to hydrostatics

Question 5

Hydrostatics (true or false):

Examines the effect of pressure applied to fluids at rest

Answer 5

True. Pascal’s experiments investigated the application of an external force to a compressed fluid.

Question 6

When a force (F) is applied to a liquid, the pressure (P) generated is (true or false):

Directly proportional to the applied force

Answer 6

True. Pressure is defined as force per unit area and is expressed in pascals (Pa).

Question 7

When a force (F) is applied to a liquid, the pressure (P) generated is (true or false):

Inversely proportional to the applied force

Answer 7

False. Pressure equals force divided by area (P = F/A).

Question 8

When a force (F) is applied to a liquid, the pressure (P) generated is (true or false):

Independent of the area (A) over which the force is applied

Answer 8

False. As pressure is equal to force divided by area (P = F/A), the pressure is inversely proportional to the area over which it is applied.

Question 9

When a force (F) is applied to a liquid, the pressure (P) generated is (true or false):

Inversely proportional to the density of the liquid

Answer 9

False. Density is not a factor in the relevant equation P = F/A.

Question 10

When a force (F) is applied to a liquid, the pressure (P) generated is (true or false):

Directly proportional to the area of the applied force

Answer 10

False. Pressure is inversely proportional to the area over which it is applied: P = F/A.

Question 11

Pascal’s observations started with a pig’s head filled with liquid. Imagine a piston applies 20 N of force to a plastic pig’s head. Two holes, each with an area of 0.02m2 are made in the otherwise sealed pig’s head. One hole is at the top of the head, one at the snout.

Regarding the escaping liquid (true or false):

It escapes at an angle of 45° to the container’s surface

Answer 11

False. The liquid escapes at an angle of precisely 90° to the surface of the vessel.

Question 12

Pascal’s observations started with a pig’s head filled with liquid. Imagine a piston applies 20 N of force to a plastic pig’s head. Two holes, each with an area of 0.02m2 are made in the otherwise sealed pig’s head. One hole is at the top of the head, one at the snout.

Regarding the escaping liquid (true or false):

It escapes at variable angles

Answer 12

False. The liquid escapes at an angle of precisely 90° to the surface of the vessel.

Question 13

Pascal’s observations started with a pig’s head filled with liquid. Imagine a piston applies 20 N of force to a plastic pig’s head. Two holes, each with an area of 0.02m2 are made in the otherwise sealed pig’s head. One hole is at the top of the head, one at the snout.

Regarding the escaping liquid (true or false):

The pressure of the jet at hole A, assuming that hole B is blocked, is 100 Pa

Answer 13

False. Pressure equals force divided by area (P = F/A). The area of the single open hole is 0.02 m2. Therefore, P = 20/0.02 = 1000 Pa = 1 kPa.

Question 14

Pascal’s observations started with a pig’s head filled with liquid. Imagine a piston applies 20 N of force to a plastic pig’s head. Two holes, each with an area of 0.02m2 are made in the otherwise sealed pig’s head. One hole is at the top of the head, one at the snout.

Regarding the escaping liquid (true or false):

Were hole B enlarged to twice the area of hole A, then the pressure at hole B would be half of that at hole A

Answer 14

True. As P = F/A, then doubling the area always halves the pressure. In this case the total area of the holes, with hole B enlarged, would be 0.06 m2. P = 20/0.06 = 333.3 Pa. Pressure at hole A (the smaller) is 222.2 Pa, and at hole B (the larger) 111.1 Pa.

Question 15

Pascal’s observations started with a pig’s head filled with liquid. Imagine a piston applies 20 N of force to a plastic pig’s head. Two holes, each with an area of 0.02m2 are made in the otherwise sealed pig’s head. One hole is at the top of the head, one at the snout.

Regarding the escaping liquid (true or false):

Its pressure on escape is unpredictable for all practical purposes, as Pascal’s principle applies only to a sphere

Answer 15

False. The shape of the vessel is not important. Indeed, Pascal’s first observations were made on hogsheads filled with wine, which was the traditional method of storage at the time.

Question 16

Consider a column of fluid with height h, density of fluid p and area A. It has two points within it, P1 at the bottom of the column and P2 half way down the column. Is the following statement true or false?

The pressure at point P1 = ρhgA

Answer 16

False. Pressure (P) = ρgh. The area of the column is not relevant to this calculation.

Question 17

Consider a column of fluid with height h, density of fluid p and area A. It has two points within it, P1 at the bottom of the column and P2 half way down the column. Is the following statement true or false?

In a column of twice the height (2h) the pressure at point P1 = ρ2hg/A

Answer 17

False. As P = ρgh, doubling the height makes the pressure greater, but the area of the column remains irrelevant.

Question 18

Consider a column of fluid with height h, density of fluid p and area A. It has two points within it, P1 at the bottom of the column and P2 half way down the column. Is the following statement true or false?

The pressure at point P2= ρ(h/2)g

Answer 18

True. P at point P2 = ρ(h/2)g.

Question 19

Consider a column of fluid with height h, density of fluid p and area A. It has two points within it, P1 at the bottom of the column and P2 half way down the column. Is the following statement true or false?

A column of twice the area (2A) would generate a pressure at point P1 of twice that generated by the column with area A

Answer 19

False. P = ρgh. The height of the column, not its area, affects the pressure.

Question 20

Consider a column of fluid with height h, density of fluid p and area A. It has two points within it, P1 at the bottom of the column and P2 half way down the column. Is the following statement true or false?

If the column were angled at 30° to the vertical the pressure at point P1 would remain the same