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2. A 10-inch x 10-inch x 0.75-inch plate casting is produced with a steel alloy with p = 0.28 lb/in³ (= 7.75 g/cm³). Two third of the steel plate casting volume should be added more into the original one, and all molten metal should be poured in 10 seconds. The cylindrical, tapered sprue height is 4 inches. The sprue has a cylindrical base and is connected to two runners. Each runner with a square vertical cross-section is connected to two gates. The gate has a rectangular vertical cross-section, and its width is three times the height. 0.75 inch Cylindrical sprue base Steel alloy casting Note that drawings are not to actual scale or ratios. Square Rectangular runner gate Cylindrical riser The ratio of the cylindrical sprue base's horizontal cross-sectional area to the sum of two runners' vertical cross-sectional areas to the sum of four gates' vertical cross-sectional areas is 1:2:3.

2. A 10-inch x 10-inch x 0.75-inch plate casting is produced with a steel alloy with p = 0.28 lb/in³ (= 7.75 g/cm³). Two third of the steel plate casting volume should be added more into the original one, and all molten metal should be poured in 10 seconds. The cylindrical, tapered sprue height is 4 inches. The sprue has a cylindrical base and is connected to two runners. Each runner with a square vertical cross-section is connected to two gates. The gate has a rectangular vertical cross-section, and its width is three times the height. 0.75 inch Cylindrical sprue base Steel alloy casting Note that drawings are not to actual scale or ratios. Square Rectangular runner gate Cylindrical riser The ratio of the cylindrical sprue base's horizontal cross-sectional area to the sum of two runners' vertical cross-sectional areas to the sum of four gates' vertical cross-sectional areas is 1:2:3.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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# Steel Plate Casting Design Overview ## Casting Details A 10-inch by 10-inch by 0.75-inch steel alloy plate casting is being designed. The steel used has a density of \( \rho = 0.28 \, \text{lb/in}^3 \) (\( = 7.75 \, \text{g/cm}^3 \)). To the original steel plate casting volume, an additional two-thirds of the volume is to be added. The entire molten metal should be poured within 10 seconds. ### Sprue, Runner, and Gate Configuration - **Sprue**: The sprue is cylindrical and tapered with a height of 4 inches. - **Base**: The sprue has a cylindrical base. - **Runners**: Two runners are connected to the sprue base. Each runner has a square vertical cross-section. - **Gates**: Each runner connects to two gates, which have a rectangular vertical cross-section. The width of each gate is three times its height. > **Note**: Drawings are illustrative and not to scale or ratio. ### Cross-Sectional Area Ratios The areas of the various components relate as follows: - The ratio of the cylindrical sprue base's horizontal cross-section area to the sum of the vertical cross-sectional areas of the two runners, and then to the sum of the vertical cross-sectional areas of four gates, is 1 : 2 : 3. ### Diagram Explanation The diagram illustrates: 1. **Cylindrical Sprue Base**: Shown as a circle representing its horizontal cross-section. 2. **Runners**: Illustrated by two adjoining squares signifying their vertical cross-sectional areas. 3. **Gates**: Represented by four adjoining rectangles. > **Note**: Diagrams focus on explaining the concept and are not drawn to actual scale or proportions.
Transcribed Image Text:# Steel Plate Casting Design Overview ## Casting Details A 10-inch by 10-inch by 0.75-inch steel alloy plate casting is being designed. The steel used has a density of \( \rho = 0.28 \, \text{lb/in}^3 \) (\( = 7.75 \, \text{g/cm}^3 \)). To the original steel plate casting volume, an additional two-thirds of the volume is to be added. The entire molten metal should be poured within 10 seconds. ### Sprue, Runner, and Gate Configuration - **Sprue**: The sprue is cylindrical and tapered with a height of 4 inches. - **Base**: The sprue has a cylindrical base. - **Runners**: Two runners are connected to the sprue base. Each runner has a square vertical cross-section. - **Gates**: Each runner connects to two gates, which have a rectangular vertical cross-section. The width of each gate is three times its height. > **Note**: Drawings are illustrative and not to scale or ratio. ### Cross-Sectional Area Ratios The areas of the various components relate as follows: - The ratio of the cylindrical sprue base's horizontal cross-section area to the sum of the vertical cross-sectional areas of the two runners, and then to the sum of the vertical cross-sectional areas of four gates, is 1 : 2 : 3. ### Diagram Explanation The diagram illustrates: 1. **Cylindrical Sprue Base**: Shown as a circle representing its horizontal cross-section. 2. **Runners**: Illustrated by two adjoining squares signifying their vertical cross-sectional areas. 3. **Gates**: Represented by four adjoining rectangles. > **Note**: Diagrams focus on explaining the concept and are not drawn to actual scale or proportions.
The height of the cylindrical riser is 1.75 times its diameter, so it takes 30% longer for the riser to solidify compared to the solidification time of the steel plate casting. The dynamic viscosity of steel is \(4 \times 10^{-3} \, \text{lb/ft/S} (= 6 \, \text{cP} = 6 \times 10^{-3} \, \text{Pa} \cdot \text{S})\), and the mold constant = \(16 \, \text{min/in}^2\). The gravitational acceleration is \(32.2 \, \text{ft/s}^2\). Determine the following, showing your work clearly: (a) Based on the problem statement, sketch an isometric view of a pattern with all components, such as sprue, sprue base, runners, gates, riser, and so on, required for this casting process. Include a label for each component. Note that the sketch is not necessary to have actual scale or ratios. (b) The cylindrical sprue base’s horizontal cross-section diameter. Note that your answer should be in [in]. (c) The dimensions of each runner’s vertical cross-section. Note that your answer should be in [in]. (d) The dimensions of each gate’s vertical cross-section. Note that your answer should be in [in]. (e) The dimensions of the cylindrical riser. Note that your answer should be in [in].
Transcribed Image Text:The height of the cylindrical riser is 1.75 times its diameter, so it takes 30% longer for the riser to solidify compared to the solidification time of the steel plate casting. The dynamic viscosity of steel is \(4 \times 10^{-3} \, \text{lb/ft/S} (= 6 \, \text{cP} = 6 \times 10^{-3} \, \text{Pa} \cdot \text{S})\), and the mold constant = \(16 \, \text{min/in}^2\). The gravitational acceleration is \(32.2 \, \text{ft/s}^2\). Determine the following, showing your work clearly: (a) Based on the problem statement, sketch an isometric view of a pattern with all components, such as sprue, sprue base, runners, gates, riser, and so on, required for this casting process. Include a label for each component. Note that the sketch is not necessary to have actual scale or ratios. (b) The cylindrical sprue base’s horizontal cross-section diameter. Note that your answer should be in [in]. (c) The dimensions of each runner’s vertical cross-section. Note that your answer should be in [in]. (d) The dimensions of each gate’s vertical cross-section. Note that your answer should be in [in]. (e) The dimensions of the cylindrical riser. Note that your answer should be in [in].
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