Question 3.1: Cartridge-Type Valve Opening and Flow Rate Assume the poppet......
Cartridge-Type Valve Opening and Flow Rate
Assume the poppet diameter of a cartridge-type flow control valve as shown in Figure 3.4 is 20 mm and the angle of poppet cone is 45°. When the poppet is lifted 3 mm by 1.5 MPa of upstream pressure, what will be the flow rate passing through the valve if the downstream of the valve is connected to the pressurized reservoir with a 0.3 MPa back pressure (assume valve orifice coefficient of 0.8 for cartridge-type valve and fluid density of 850 kg · m^{-3} for hydraulic fluids).
a. The orifice area of the valve can be calculated using Eq. (3.4):
A_{\circ }=\pi dx \sin \alpha
= 3.14 \times 2.0\times 0.3\times \sin (45^{\circ} )
= 1.33 (cm^{2})
b. The flow rate passing through this valve can be calculated using Eq. (3.2):
Q=A_{\circ}C_{d}\sqrt{\frac{2}{\rho } \Delta P}
= 1.33\times 10^{-4}\times 0.8\times \sqrt{\frac{2}{850} \times 1.2\times 10^{6}}
=5.65\times 10^{-3} (m^{3}\cdot s^{-1}) = 339 (L\cdot min^{-1})
DISCUSSION 3.1: An orifice area of a valve is determined by the geometric configuration of the valve flow control element within a valve body, as does the orifice coefficient. The flow rate controlled by the valve can be reasonably estimated using an orifice equation.