The centerline of a nozzle is to be placed at 58 degrees from top dead center (TDC) on a tank with a measured circumference of 540″. How many inches from TDC is the centerline of the nozzle to be located?
Group of answer choices
58 inches
76 1/4 inches
110 3/16
140 inches
87 inches
To calculate the distance from TDC, we first need to find the fraction of the circumference that corresponds to the 58-degree angle.
We know that a full circle has a circumference of 540″.
To find the fraction of the circumference, we can use the formula:
angle/360 = fraction of circumference/total circumference
In this case, the angle is 58 degrees and the total circumference is 540″.
58/360 = fraction of circumference/540
Simplifying, we get:
0.1611 = fraction of circumference/540
To find the fraction of the circumference, we multiply both sides of the equation by 540:
0.1611 * 540 = fraction of circumference
Approximately, this is equal to:
87.094 inches = fraction of circumference
So, the centerline of the nozzle should be located approximately 87 inches from TDC.
Therefore, the correct answer is 87 inches.
To calculate the distance of the centerline of the nozzle from the top dead center (TDC), we can use the following formula:
Distance = (Angle / 360) * Circumference
Given:
Angle = 58 degrees
Circumference = 540 inches
Plugging in the values into the formula:
Distance = (58 / 360) * 540
Simplifying the calculation:
Distance = (0.1611) * 540
Distance = 87 inches
Therefore, the centerline of the nozzle should be located 87 inches from TDC.
To find the distance from TDC to the centerline of the nozzle, we can use the concept of the circumference of a circle.
1. The measured circumference of the tank is 540". We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
So, C = 2πr = 540"
Dividing both sides of the equation by 2π, we get:
r = 540" / (2π) ≈ 85.94" (approximately)
2. Now, let's consider the angle of 58 degrees from TDC. Since there are 360 degrees in a circle, we can calculate the ratio of the angle to the total circumference:
Angle/360 = Distance from TDC/Circumference
58/360 = Distance from TDC/540"
Solving for Distance from TDC, we get:
Distance from TDC = (58/360) * 540" ≈ 87" (approximately)
Therefore, the centerline of the nozzle should be located approximately 87 inches from TDC.