A Diesel Engine's Day Tank Volume and Dimensions Calculation

What is the volume of a cylindrical day tank needed for continuous operation of a diesel engine consuming fuel at a rate of 180 kg per hour with an API of 28° at an atmospheric temperature of 35°C? What are the dimensions of the cylindrical tank if the height is twice the diameter?

Calculating the Cylindrical Day Tank Volume and Dimensions

API Gravity Conversion: To begin, we need to convert the API gravity of 28° to specific gravity (SG) using the formula SG = (141.5 / API) + 131.5. Calculating, we get SG = (141.5 / 28) + 131.5 = 5.05357. Density Calculation: Next, we calculate the density of the fuel using specific gravity and the density of water at 35°C (approximately 997.77 kg/m³). Density = SG * ρ_water = 5.05357 * 997.77 = 5029.68 kg/m³. Fuel Consumption Volume: Given the fuel consumption rate of 180 kg/hour, we divide the mass by density to find the volume consumed per hour: Volume = 180 kg / 5029.68 kg/m³ ≈ 0.0358 m³/hour. Cylindrical Tank Volume Calculation: Using the volume formula for a cylinder (V = π * (D/2)² * H), and given the volume as 0.0358 m³ and height as twice the diameter, we find the diameter of the tank to be approximately 0.2966 meters and the height as 0.5932 meters. Therefore, the cylindrical day tank volume needed for continuous operation is 4.944 cubic meters. The dimensions of the tank are approximately 0.2966 meters in diameter and 0.5932 meters in height.

How does the API gravity of the diesel fuel and its consumption rate contribute to determining the required volume and dimensions of the cylindrical day tank for a diesel engine's continuous operation?

Understanding the Impact of API Gravity and Fuel Consumption Rate

API Gravity and Density: The API gravity of the diesel fuel (28°) influences its specific gravity, which in turn affects its density. Higher API gravity indicates lighter density, thus impacting the volume of fuel consumed per hour. Fuel Consumption Rate: The rate at which the diesel engine consumes fuel, in this case 180 kg per hour, directly determines the volume of fuel needed to sustain continuous operation. This consumption rate, coupled with the fuel density, guides the calculation of the required volume of the cylindrical day tank. Volume and Dimensions Calculation: By converting API gravity to specific gravity, calculating density, and determining the fuel consumption volume, we can accurately estimate the volume of the day tank. The specifications of the tank, such as its height being twice the diameter, further refine the dimensions calculation for optimal fuel storage capacity. Therefore, the API gravity and consumption rate play crucial roles in defining the volume and dimensions of the cylindrical day tank for efficient and continuous operation of a diesel engine.

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