Answer:
Yes, fracture will occur
Explanation:
Half length of internal crack will be 4mm/2=2mm=0.002m
To find the dimensionless parameter, we use critical stress crack propagation equation
and making Y the subject

Where Y is the dimensionless parameter, a is half length of crack, K is plane strain fracture toughness,
is critical stress required for initiating crack propagation. Substituting the figures given in question we obtain

When the maximum internal crack length is 6mm, half the length of internal crack is 6mm/2=3mm=0.003m
and making K the subject
and substituting 260 MPa for
while a is taken as 0.003m and Y is already known

Therefore, fracture toughness at critical stress when maximum internal crack is 6mm is 42.455 Mpa and since it’s greater than 40 Mpa, fracture occurs to the material
Answer:
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Answer:
the heat transfer from the pipe will decrease when the insulation is taken off for r₂< 
where;
r₂ = outer radius
= critical radius
Explanation:
Note that the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h .

The rate of heat transfer from the cylinder increases with the addition of insulation for outer radius less than critical radius (r₂<
) 0, and reaches a maximum when r₂ =
, and starts to decrease for r₂<
. Thus, insulating the pipe may actually increase the rate of heat transfer from the pipe instead of decreasing it when r₂<
.
Answer:
The pipe is open ended and the length of pipe is 3.4 m.
Explanation:
For identification of the type of pipe checking the successive frequencies in both the open pipe and closed pipe as below
Equation for nth frequency for open end pipe is given as

For (n+1)th value the frequency is

Taking a ratio of both equation and solving for n such that the value of n is a whole number

So n is a whole number this means that the pipe is open ended.
For confirmation the nth frequency for a closed ended pipe is given as

For (n+1)th value the frequency is

Taking a ratio of both equation and solving for n such that the value of n is a whole number

As n is not a whole number so this is further confirmed that the pipe is open ended.
Now from the equation of, with n=6, v=340 m/s and f=300 Hz

The value of length is 3.4m.