In a direct acting pressure relief valve, 64 bar pressure is acting on the conical dart seating area and the dart is kept closed by a spring force of 50 kg opposing the pressure.
a) Determine the bore diameter on the seat.
b) What will the spring force be if a pressure of 3200 kPa is acting on diameter of 10 mm seating area?
a) To determine the bore diameter on the seat, we can use the formula for the force on the dart in a direct acting pressure relief valve:
Force = Pressure * Area
Given:
Pressure = 64 bar
Force = 50 kg
We need to convert the pressure from bar to pascals (1 bar = 100,000 pascals):
Pressure = 64 bar * 100,000 pascals/bar = 6,400,000 pascals
Now, we can rearrange the formula to solve for the area:
Area = Force / Pressure
Plugging in the values:
Area = 50 kg / 6,400,000 pascals
To convert the force from kg to newtons (1 kg = 9.8 newtons):
Area = (50 kg * 9.8 newtons/kg) / 6,400,000 pascals
Simplifying:
Area = 0.078125 * 10^-3 m²
To find the bore diameter on the seat, we can use the formula for the area of a circle:
Area = π * (Diameter/2)^2
Rearranging the formula to solve for the diameter:
Diameter = 2 * (√(Area/π))
Plugging in the value:
Diameter = 2 * (√(0.078125 * 10^-3/π))
Now, we can calculate the diameter:
Diameter ≈ 0.01 m or 10 mm
Therefore, the bore diameter on the seat is approximately 10 mm.
b) To find the spring force when a pressure of 3200 kPa is acting on a diameter of 10 mm seating area, we can use the same formula for force:
Force = Pressure * Area
Given:
Pressure = 3200 kPa
Diameter = 10 mm
First, we need to convert the pressure from kPa to pascals (1 kPa = 1000 pascals):
Pressure = 3200 kPa * 1000 pascals/kPa = 3,200,000 pascals
Next, we can calculate the area using the diameter:
Area = π * (Diameter/2)^2
Plugging in the values:
Area = π * (10 mm/2)^2
Area = π * 5^2 mm²
To convert the area from square millimeters to square meters:
Area ≈ 78.54 * 10^-6 m²
Finally, we can calculate the spring force:
Force = Pressure * Area
Force = 3,200,000 pascals * 78.54 * 10^-6 m²
Force ≈ 251.32 newtons
Therefore, the spring force when a pressure of 3200 kPa is acting on a diameter of 10 mm seating area is approximately 251.32 newtons.