Exercises Hydrostatics

Solution A1: hydraulic press:

1.   W1  =  W2    ⇒    F1  *  d1   = F2 * d2 = 30 Nm  ⇒  F2 = 30 Nm / 0,0011 m  = 27,27 kN

F2 stands for the weight of the mass, which is lifted by the load piston:

F_G = F₂ = m * g   ⇒  m = F₂ / g = 27,27 kN / 9,81 m/s²  =  2779,82 kg

2.  Solution:   d₂ = 200 mm

3.   p₂ = F₂ / A₂  =  27270 N / 314,15 cm²  = 136,01 bar = 1,3601 * 10⁷ Pa = 13,601 MPa

Solution A2: hydraulic brake system

F_Pedal * d_Pedal/2  =    F_Piston* s_{contact point}        (one side level)

=>      F_piston   =   F_Pedal  * s_Pedal/2   =   60 N * 15 cm  = 90 N
.                                  s_{contact point}                 10 cm

Pressure within the system: p = F_Piston  / A_Piston =   90 N /5 cm²   =  18 N / cm²  =  1,8 bar

F_{Brake pad} = p * A_{Brake pad}                              , A_{Brake pad} = (ᴫ d²_{Brake pad}) / 4= ᴫ 5² cm²  / 4=  19,63 cm²

F_{Brake pad} = 18 N / cm²  * 19,63 cm² =   353,34 N

Total brake force = 2 * F_{Brake pad} = 2* 353,34 N = 706,68 N