Question

A pressure gauge is connected to the working chamber of Cylinder 1 and measures its pressure P1.
A force F1 is acting on the piston push rod in the direction shown in the figure, with a magnitude of 100 Newtons.
The diameter of Cylinder 1 is given as 45mm.
Q: Calculate the magnitude of pressure P1 resulting from the force on the piston F1.
Give your answer in Pa.

Answer 1

Answer on Question #49045-Engineering-Other

A pressure gauge is connected to the working chamber of Cylinder 1 and measures its pressure P1. A force F1 is acting on the piston push rod in the direction shown in the figure, with a magnitude of 100 Newtons. The diameter of Cylinder 1 is given as 45mm. Calculate the magnitude of pressure P1 resulting from the force on the piston F1. Give your answer in Pa.

Solution

The magnitude of pressure $P_{1}$ resulting from the force on the piston $F_{1}$ is

$$P_{1} = \frac{F_{1}}{A_{1}},$$

where $A_{1} = \frac{\pi d_{1}^{2}}{4}$ is the area of Cylinder 1, $d_{1} = 45\mathrm{mm} = 45\cdot 10^{-3}m$ is diameter of Cylinder 1.

Thus

$$P_{1} = \frac{F_{1}}{\frac{\pi d_{1}^{2}}{4}} = \frac{4\cdot 100\mathrm{N}}{\pi(45\cdot 10^{-3}m)^{2}} = 63\cdot 10^{3}\mathrm{Pa} = 63000\mathrm{Pa}.$$

Answer: $63 \cdot 10^{3} \mathrm{~Pa} = 63000 \mathrm{~Pa}$.

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