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Answer :
(a) Clearance volume: 1098.97 cubic cm (67.11 cubic inches). (b) Bore: 22.64 cm (8.92 inches). Stroke: 24.01 cm (9.45 inches).
To solve these calculations, let's break them down step by step:
(a) Clearance volume of one cylinder in cubic cm, L, and cubic inches:
The clearance volume (Vc) of one cylinder can be calculated using the following formula:
[tex]\[V_c = \frac{V_s}{CR - 1}\][/tex]
Where:
[tex]- \(V_s\) = Swept volume of one cylinder[/tex]
[tex]- \(CR\) = Compression Ratio[/tex]
First, we need to find the swept volume (Vs) of one cylinder:
[tex]\[Vs = \frac{\pi}{4} \times B^2 \times S\][/tex]
Given:
- Bore (B) = ?
- Stroke (S) = ?
We know that the bore and stroke are related as [tex]\(S = 1.06B\)[/tex].
Let's calculate the values of bore (B) and stroke (S):
[tex]\[S = 1.06B\][/tex]
[tex]\[S = 1.06 \times B\][/tex]
[tex]\[B = \frac{S}{1.06}\][/tex]
Substituting the given value of stroke, [tex]\(S = 1.06 \times B\)[/tex], we can solve for B:
[tex]\[3200 = \frac{2.12B}{2} \times \frac{4}{60}\][/tex]
[tex]\[3200 = 2.12B \times \frac{4}{60}\][/tex]
[tex]\[3200 = 0.1413B\][/tex]
[tex]\[B \approx 226.37\][/tex]
Now, we can find the stroke (S):
[tex]\[S = 1.06 \times 226.37\][/tex]
[tex]\[S \approx 240.10\][/tex]
Now that we have the values of Bore (B) and Stroke (S), we can calculate the swept volume (Vs):
[tex]\[Vs = \frac{\pi}{4} \times (226.37)^2 \times 240.10\][/tex]
[tex]\[Vs \approx 9,238,703.96 \text{ cubic mm}\][/tex]
Now, we can find the clearance volume (Vc) using the compression ratio (CR):
[tex]\[CR = \frac{V_s + V_c}{V_c}\][/tex]
[tex]\[9.4 = \frac{9,238,703.96 + V_c}{V_c}\][/tex]
Now, solve for [tex]\(V_c\):[/tex]
[tex]\[V_c \times 9.4 = 9,238,703.96 + V_c\][/tex]
[tex]\[8.4V_c = 9,238,703.96\][/tex]
[tex]\[V_c \approx 1,098,965.23 \text{ cubic mm}\][/tex]
Now, convert the clearance volume to cubic inches:
[tex]\[1,098,965.23 \text{ cubic mm} \approx 67.11 \text{ cubic inches}\][/tex]
(b) Bore and stroke in cm and inches:
Bore (B) in cm:
[tex]\[B \approx 226.37 \text{ mm} = 22.637 \text{ cm}\][/tex]
Stroke (S) in cm:
[tex]\[S \approx 240.10 \text{ mm} = 24.010 \text{ cm}\][/tex]
Now, let's convert these values to inches:
[tex]\[1 \text{ inch} \approx 2.54 \text{ cm}\][/tex]
Bore (B) in inches:
[tex]\[22.637 \text{ cm} \div 2.54 = 8.92 \text{ inches}\][/tex]
Stroke (S) in inches:
[tex]\[24.010 \text{ cm} \div 2.54 = 9.45 \text{ inches}\][/tex]
So, to summarize:
(a) Clearance volume of one cylinder:
- In cubic cm: [tex]\(1,098,965.23\)[/tex]
- In cubic inches: [tex]\(67.11\)[/tex]
(b) Bore and stroke:
- Bore: [tex]\(22.637 \text{ cm}\) or \(8.92 \text{ inches}\)[/tex]
- Stroke: [tex]\(24.010 \text{ cm}\) or \(9.45 \text{ inches}\)[/tex]
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