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Masja [62]
3 years ago
12

Determine size of a standard square key made of 1045 hot rolled steel for a 2 inch DIA shaft transmitting 100 HP at 500 rpm with

factor of safety 2.5 for yield in direct shear. W____inch L_____inch
Engineering
1 answer:
user100 [1]3 years ago
3 0

Answer:

Width = Length = 1.148 inches

Explanation:

We have been given the following data:

D = diameter = 2 inch = 0.0508m

P = Power = 100 HP = 74570 W

N = 500 rpm

Safety Factor = 2.5

<h3>Step 1:</h3>

We need to find yield strength which is represented by σ(y).

σ(y) for 1045 hot rolled steel = 330MPa

<h3 /><h3>Step 2: </h3>

Find Shear Strength. Formula is given:

τ(y) = σ(y) / 2

τ(y) = 330 / 2

τ(y) = 165 MPa

τ(y) = 165 × 10⁶ Pa

τ(y) = 165 × 10⁶ kg.m⁻¹.s⁻²

<h3>Step 3:</h3>

Find Torque. Formula is given:

T = 60P / 2πN

T= (60)(74570) / 2π(500)

T = 1424.9 Nm

<h3 /><h3>Step 4:</h3>

Find Shear Force. Formula is given:

F = 2T/d

F = 2(1424.9)/0.0508

F = 56098.43 N

F = 56098.43 kg.m.s⁻²

<h3 /><h3>Step 5:</h3>

Find length by the given formula:

F/L² = τ(y)/Safety factor

Rearrange for L:

L = √(F· Safety factor / τ(y))

Substitute the values found in previous steps to calculate L.

L = 0.02915 meters

Convert it into inches:

L = 1.148 in

As it si a square key:

L = W

Width = 1.148 in

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A rectangular car-top carrier of 1.7-ft height, 5.0-ft length (front to back), and 4.2-ft width is attached to the top of a car.
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The last formula is without consider the area of the carrier, but if we use the area for the carrier we got:

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If we want to find the additional power added with the carrier we just need to take the difference between the multiplication of drag force by the velocity (assuming equal velocities for both cases) of the two cases, and we got:

\Delta P = C_{D2} \frac{\rho}{2}V^2 (wh+ A_{carrier}) V-  C_{D1} \frac{\rho}{2}V^2 (wh) V

We can assume the same drag coeeficient C_{D1}=C_{D2}=C_{D} and we got:

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And the value for the kinematic vicosity was obtained from the table of physical properties of the air under standard conditions.

Now we can find the aspect ratio like this:

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And we can estimate the calue of C_D = 1.2 from a figure.

And we can calculate the power difference like this:

\Delta P =1.2 \frac{1.3}{2}(26.822m/s)^2 (4.2*1.7*(0.3048)^2)=13.88 hp

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