Answer:
d=0.1456m =145.64mm
Explanation:
Conceptual analysis :
To solve this problem we consider the following concepts:
1)The force on a fluid is calculated as follows:
F = P*A Formula (1)
F: The force at a certain height in the fluid in (N)
P: Pressure in units of force per unit of area(N/m^2) (Pascal) (Pa)
A: cross sectional area (m2)
2) In a piston, the cross-sectional area (A) is the area of a circle and is calculated using the following formula:
[tex]A = \frac{\pi d^{2} }{4}[/tex] Formula (2)
d: piston/cylinder diameter in (m)
3)The weight of an object (W) is calculated using the following formula:
W=m*g
Where:
W: Weight in Newtons(N)
m = mass in kg
g = acceleration due to gravity in m/s
Known information :
We know the following data:
P = 500 kPa = 500*10^3 Pa = 5*10^5 Pa
m =850 kg
Development of the problem :
[tex]F=W=m*g=850kg*9.8\frac{m}{s^2} =8330N[/tex]
[tex]A=\frac{\pi*d^2}{4}[/tex]
In the formula 1:
F=P*A
[tex]8330=(5*10^5)* \frac{\pi*d^2}{4}[/tex]
[tex]d^2=\frac{4*8330}{\pi*5*10^5}[/tex]
[tex]d=\sqrt{\frac{4*8330}{\pi*5*10^5}}[/tex]
d=0.1456m
d=145.64mm
