Measurement of Pressure

1. Project: Measurement of
Pressure
MECH 1502: Mechanical Engineering
Science II
Done by: Raheem E. C. Cole

2. 03 Pressure
Absolute
Pressure
04
Principles of
Pressure
Exerted by a
Liquid
05
Principle of a
Hydraulic
Machine
06
07
Operating
Principle of a
Manometer
08 Question 3
12 Question 10
15 References

3. Pressure
❏ defined as a measure of the force applied
over a unit area
❏ is a scalar quantity
❏ expressed in units of Pascals (Pa), newtons
per square meter (N/m2 or kg/m·s2), or
pounds per square inch, atmosphere (atm),
torr, bar, and meters sea water (msw).
❏ pressure is denoted by the capital letter P

4. Absolute Pressure
❏ is a pressure that is relative to the zero
pressure in air-free space
❏ This pressure references the ideal vacuum
❏ expressed in the formula Pabs=Patm+Pguage
or Pabs= Phead + Patm

5. Principles of Pressure Exerted
by a Liquid
❏ Means the vertical distance of the
liquid’s surface
❏ The normal force exerted by a liquid
per unit area
❏ Known as hydrostatic pressure
❏ Pressure will be the same at all
points at the same level in all
directions
❏ Pressure exerted is always
perpendicular to its surface

6. Principle of a Hydraulic
Machine
❏ Follows Pascal’s law

7. Operating Principle of a
Manometer
❏ Changes in pressure affects liquid
height

8. Question 3
3) A hydraulic accumulator with a ram of 400mm in
diameter is connected with a hydraulic press whose
ram is 800mm in diameter. The load on the
accumulator is 700 kN.
a. What is the pressure, in kN/m2 on the ram of the
accumulator?
b. What total force, in kN, would the press exert?
c. Calculate the head equivalent to the pressure on
the ram of the accumulator.

9. - 𝐷𝑎𝑐𝑐 = 400𝑚𝑚 𝑜𝑟 0.4𝑚; 𝐷𝑝𝑟𝑒𝑠𝑠800𝑚𝑚 𝑜𝑟 0.8𝑚; 𝐹𝑎𝑐𝑐 = 700𝑘𝑁
a. What is the pressure, in kN/m2 on the ram of the accumulator?
- 𝑃𝑎𝑐𝑐 =
𝐹𝑎𝑐𝑐
𝐴
𝑃𝑎𝑐𝑐 =
𝐹𝑎𝑐𝑐
𝜋
4
× 𝐷𝑎𝑐𝑐
2
𝑃𝑎𝑐𝑐 =
700𝑘𝑁
𝜋
4
× 0.4𝑚 2
𝑃𝑎𝑐𝑐 =
700𝑘𝑁
𝜋
4
× 0.16𝑚2
𝑃𝑎𝑐𝑐 =
700𝑘𝑁
𝜋 × 0.04𝑚2
𝑃𝑎𝑐𝑐 =
700𝑘𝑁
0.125663706𝑚2
𝑷𝒂𝒄𝒄 = 𝟓, 𝟓𝟕𝟎. 𝟒 𝒌𝑵/𝒎𝟐

10. - 𝐷𝑎𝑐𝑐 = 400𝑚𝑚 𝑜𝑟 0.4𝑚; 𝐷𝑝𝑟𝑒𝑠𝑠800𝑚𝑚 𝑜𝑟 0.8𝑚; 𝐹𝑎𝑐𝑐 = 700𝑘𝑁
b. What total force, in kN, would the press exert?
- 𝑃𝑝𝑟𝑒𝑠𝑠 =
𝐹𝑝𝑟𝑒𝑠𝑠
𝐴
𝐹𝑝𝑟𝑒𝑠𝑠 = 𝑃𝑝𝑟𝑒𝑠𝑠 𝐴
𝐹𝑝𝑟𝑒𝑠𝑠 = 𝑃𝑝𝑟𝑒𝑠𝑠
𝜋
4
× 𝐷𝑝𝑟𝑒𝑠𝑠
2
𝐹𝑝𝑟𝑒𝑠𝑠 = 5,570.4 𝑘𝑁/𝑚2
𝜋
4
× 0.8𝑚 2
𝐹𝑝𝑟𝑒𝑠𝑠 = 5,570.4 𝑘𝑁/𝑚2
𝜋
4
× 0.64𝑚2
𝐹𝑝𝑟𝑒𝑠𝑠 = 5,570.4 𝑘𝑁/𝑚2
𝜋 × 0.16𝑚2
𝐹𝑝𝑟𝑒𝑠𝑠 = 5,570.4 𝑘𝑁/𝑚2
0.5026548246𝑚2
𝑭𝒑𝒓𝒆𝒔𝒔 = 𝟐, 𝟖𝟎𝟎𝒌𝑵

11. - 𝐷𝑎𝑐𝑐 = 400𝑚𝑚 𝑜𝑟 0.4𝑚; 𝐷𝑝𝑟𝑒𝑠𝑠800𝑚𝑚 𝑜𝑟 0.8𝑚; 𝐹𝑎𝑐𝑐 = 700𝑘𝑁
c. Calculate the head equivalent to the pressure on the ram of the accumulator.
𝑃ℎ𝑒𝑎𝑑 =
𝑃𝑟𝑎𝑚
𝛾𝑓𝑙𝑢𝑖𝑑
𝑃ℎ𝑒𝑎𝑑 =
5,570.4𝑘𝑁/𝑚2
9.81𝑘𝑁/𝑚3
𝑷𝒉𝒆𝒂𝒅 = 𝟓𝟔𝟕. 𝟖𝟑𝒎

12. Question 10
10) Details of mercury
manometer readings are given
below. Calculate the absolute
pressure of the water in the
pipe if the atmospheric
pressure is 1 bar.

13. 𝑃𝑎𝑡𝑚 = 1 𝑏𝑎𝑟; 150𝑚𝑚 × 1,000 = 0.15𝑚; 300𝑚𝑚 × 1,000 = 0.3𝑚
𝐺𝑢𝑎𝑔𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑡 𝑤𝑎𝑡𝑒𝑟 𝑝𝑖𝑝𝑒 = 𝜌𝑤𝑎𝑡𝑒𝑟 × 𝑔 × 0.15𝑚 + 𝜌𝐻𝑔 × 𝑔 × 0.3𝑚
𝐺𝑢𝑎𝑔𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 1,000
𝑘𝑔
𝑚3 × 9.81
𝑚
𝑠2 × 0.15𝑚 + 13,600
𝑘𝑔
𝑚3 × 9.81
𝑚
𝑠2 × 0.3𝑚
𝐺𝑢𝑎𝑔𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 1,471.5 + 40,024.8
𝐺𝑢𝑎𝑔𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
41,496.3𝑃𝑎
105
𝐺𝑢𝑎𝑔𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝟎. 𝟒𝟏𝟒𝟗𝟔𝟑𝒃𝒂𝒓
𝑷𝒂𝒕𝒎 = 𝑷𝒈𝒖𝒂𝒈𝒆 + 𝑷𝒂𝒕𝒎

14. *Link*

15. REFERENCES
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Augustyn, A. (n.d.). Pascal's principle. Encyclopædia Britannica. Retrieved May 2, 2022,
from https://www.britannica.com/science/Pascals-principle
Beyer, M. (2019, July 31). Gauge pressure & absolute pressure: Differences. WIKA blog.
Retrieved May 2, 2022, from https://blog.wika.com/knowhow/difference-between-
gauge-pressure-and-absolute-pressure-measurement/
Laxmi. (2020, September 14). Pressure exerted by the liquid - hydrostatics. Learn Cram.
Retrieved May 2, 2022, from https://www.learncram.com/physics/pressure-exerted-
by-liquid/
Mortenson, T. (2021, October 31). Manometer explained: Manometer working principle.
RealPars. Retrieved May 2, 2022, from https://realpars.com/manometer/
Yogichaudhary. (n.d.). What is the principle of a hydraulic machine??? - brainly.in.
Retrieved May 3, 2022, from https://brainly.in/question/5181982