To determine the gas accumulator capacity, we need to consider the factors of adiabatic and isothermal correction for pressures above 200 bar, as well as the temperature range of operation. Let's calculate each step of the process:
1. Determine the precharge pressure:
The precharge pressure is 95% of the minimum pressure. The minimum pressure is 208 bar, so the precharge pressure is 0.95 * 208 bar = 197.6 bar.
2. Calculate the correction factors for adiabatic and isothermal conditions:
Given that Ca = 0.72 and Ci = 0.83, we will use these values for the correction factors.
3. Calculate the corrected discharge volume:
Since the discharge volume is given as 4.6 liters, we need to correct it using the correction factors.
For adiabatic correction: Corrected discharge volume (Vd_adia) = 4.6 liters * Ca = 4.6 liters * 0.72 = 3.312 liters.
For isothermal correction: Corrected discharge volume (Vd_iso) = 4.6 liters * Ci = 4.6 liters * 0.83 = 3.818 liters.
We will use these corrected discharge volumes in the next steps to account for the factors of adiabatic and isothermal correction.
4. Calculate the capacity using the corrected discharge volumes:
The capacity is the volume of fluid discharged per unit change in pressure. To calculate it, we need to convert the discharge volumes to cubic meters:
Vd_adia = 3.312 liters = 0.003312 m³
Vd_iso = 3.818 liters = 0.003818 m³
The capacity (C) is given by the formula: C = Vd / (P1 - P2), where P1 and P2 are the initial and final pressures.
For adiabatic correction:
C_adia = Vd_adia / (P1_adia - P2_adia)
C_adia = 0.003312 m³ / (280 bar - 208 bar)
For isothermal correction:
C_iso = Vd_iso / (P1_iso - P2_iso)
C_iso = 0.003818 m³ / (280 bar - 208 bar)
5. Convert the pressures to Pascals:
To convert bar to Pascals, we multiply by 100,000.
P1_adia = 280 bar * 100,000 Pa/bar = 28,000,000 Pa
P1_iso = 280 bar * 100,000 Pa/bar = 28,000,000 Pa
P2_adia = 208 bar * 100,000 Pa/bar = 20,800,000 Pa
P2_iso = 208 bar * 100,000 Pa/bar = 20,800,000 Pa
6. Calculate the capacity:
C_adia = 0.003312 m³ / (28,000,000 Pa - 20,800,000 Pa)
C_iso = 0.003818 m³ / (28,000,000 Pa - 20,800,000 Pa)
7. Calculate the charging time:
The charging time is given as 4 minutes. To convert it to seconds, we multiply by 60.
Charging time = 4 minutes * 60 seconds/minute = 240 seconds
8. Determine the capacity taking into account the pressure and temperature ranges:
Since the specified pressure range is above 200 bar, and the temperature range is 20 °C to 50 °C, we can use the capacity calculated in step 6 without any additional correction factors.
Therefore, the final capacity of the gas accumulator is C = C_adia = 0.003312 m³ / (28,000,000 Pa - 20,800,000 Pa).
A gas accumulator should discharge 4.6 liters of fluid for a period of 3 seconds with a pressure change from 280 bar to 208 bar. Charging time is 4 minutes. Define the capacity taking into account the factors of adiabatic and isothermal correction for pressures more of 200 bar and that the temperature range of operation is 20 ° C to 50 ° C. Assume that the precharge pressure is 95% of the minimum pressure. Assume Ca = 0.72 and Ci = 0.83.
1 answer