Calculating Height Difference h of Hydraulic System Pistons

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In a hydraulic system with two pistons of different diameters and masses, the height difference (h) between the pistons can be calculated using their respective pressures. The left piston has a diameter of 4.5 cm and a mass of 1.7 kg, while the right piston has a diameter of 12 cm and a mass of 2.5 kg. The calculated pressure for each piston shows that the height difference h is approximately 3.55 meters. However, a correction was noted regarding the area calculation, leading to a revised height difference of 1.13 meters. Accurate calculations are essential for determining the correct height difference in hydraulic systems.
mikep
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In a hydraulic system the piston on the left has a diameter of 4.5 cm and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 2.5 kg. If the density of the fluid is 750 kg/m3, what is the height difference h between the two pistons?
can someone please help me with this?
A_1 = (3.14)(0.045m/2)^2 = 0.000506m^2
A_2 = (3.14)(0.12m/2)^2 = 0.0036m^2
P_1 = mg/A_1 = (1.7kg)(9.8N/kg)/0.00506m^2 = 32924.9
P_2 = mg/A_2 = (2.5kg)(9.8N/kg)/0.0036m^2 = 6805.56
P_1 - P_2 = (\rho)(h)(g)
h = (P_1 - P_2)/(\rho)(g)
h = 3.55m
 
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What help do you need? You have the right answer.

I assume that the cylinders are connected at the bottom and the fluid is not flowing through that connection. This means that the pressure at the bottom of each cylinder is the same. Since the pressure at the bottom of each is:

P = F/A = (mg + \rho Vg)/A where V = volume = hA

the condition for no flow is:

P_1 = P_2 so:

m_1g/A_1 + \rho h_1g = m_2g/A_2 + \rho h_2g

m_1/A_1 + \rho h_1 = m_2/A_2 + \rho h_2

m_1/A_1 - m_2/A_2 = \rho (h_2 - h_1)

\Delta h = (m_1/A_1 - m_2/A_2)/\rho)

AM
 
are you sure cause i got the answer wrong so i thought i did something wrong. i think i made a wrong assumetion somewhere
 
Last edited:
mikep said:
are you sure cause i got the answer wrong so i thought i did something wrong. i think i made a wrong assumetion somewhere

I was using your values for area of the pistons, but I see that you forgot to multiply by \pi. So divide your answer by 3.14 (1.13 m).

AM
 
oh and i had it setup right too. thanks
 
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