Question

Explain why the failure of this garden hose occurred near its end and why the tear occurred along its length. Use numerical values to explain your result. Assume the water pressure is 30 psi.

Answer 1

The reason for failure of hose along its length is because the hoop stress is greater than longitudinal stress.

Step-by-step explanation:

Cnverting Pressure units from Psi to Megapascal 30 Psi (Psi). = 0.20684 Megapascal (MPa).

Assume any thin cylinder pressure vessel and calculate the value of hoop and longitudinal stress.

Take the numerical values of the pipe as follows:

d = 20 mm

t = 1 mm

Here, d is the inner diameter and t is the thickness of the pipe.

Calculate the value of d / t

d/t = 20/1

= 20

The above value is greater than or equal to 20, hence it is a thin pressure vessel.

Calculate the hoop stress in the pipe.

`\sigma _1 = (pd)/(2t)`

Substitute 0.2 MPa for p, 20 mm for d and 1 mm for t

`\sigma _1 = (0.2 * 20)/(2 * 1) \\= 2MPa`

Calculate the longitudinal stress.

`\sigma _1 = (pd)/(4t)`

`\sigma _1 = (0.2 * 20)/(4 * 1) \\= 1MPa`

After doing the calculations we find that the hoop stress is greater than the longitudinal stress, hence the failure will occur due to hoop stress, or we can say the direction of tear will be along the longitudinal axis.

From the above two results we can see that the value of normal stress is higher for hoop stress, hence the failure will occur in hoop or circumferential direction.

Hence, the reason for failure of hose along its length is because the hoop stress is greater than longitudinal stress.

The reason for failure of hose along its length is because the hoop stress is greater than longitudinal stress.