A bicycle tire that has a slow leak,

• pentazoid
In summary, the conversation discusses estimating the rate at which gas escapes through a hole in a container and the size of a hole in a bicycle tire that causes it to go flat within an hour. The equations provided for this problem are N(t)=N(0)exp(-t/tau) and dN/dt=-A/2V*sqrt(kT/m)*N. However, there is confusion about the meaning of "flat" and the variable of volume in the equations. The derivation of the second equation is also unclear.
pentazoid

Homework Statement

If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a rough estimate of the rate at which gas escapes through a hole.

Your bicycle tire has a slow leak, so that it goes flat within about an hour after being inflate. Rougly how big is the hole? (use any reasonable estimate for the volume of the tire.)

Homework Equations

N(t)=N(0)exp(-t/tau), tau being the characteristic time.
dN/dt=-A/2V*sqrt(kT/m)*N

The Attempt at a Solution

By rouglhly how big is the hole, do they want me to guesstimate the volume of the tire?

Did anyone not understand my question or solution?

I did not. It's not clear to me what is meant by the tire becoming flat. V=0?
In this case, volume should be a variable. Which should mean that you can't integrate the second equation and get the first one. So they contradict each other. Can you tell me how the second equation is derived? That is, what is the situation for which it holds?

1. How can I tell if my bicycle tire has a slow leak?

One way to tell if your bicycle tire has a slow leak is by checking the tire pressure. If the tire pressure decreases significantly over a short period of time, it may indicate a slow leak. You can also try submerging the tire in water and looking for bubbles, which would indicate a leak.

2. What causes a bicycle tire to have a slow leak?

A slow leak in a bicycle tire can be caused by various factors, such as punctures from sharp objects, worn out tire tread, or damage to the tire valve. It can also be a result of poor maintenance, such as not checking and inflating the tires regularly.

3. How can I fix a slow leak in my bicycle tire?

The best way to fix a slow leak in your bicycle tire is by patching the puncture or replacing the damaged tire. You can also try using a sealant or self-sealing inner tube, but these may only provide temporary solutions. It is important to properly identify and fix the source of the leak to prevent further issues.

4. Can I still ride my bike with a slow leak in the tire?

It is not recommended to ride your bicycle with a slow leak in the tire. Not only can it make your ride more difficult and uncomfortable, but it can also cause further damage to the tire and increase the risk of a blowout. It is best to address the issue as soon as possible.

5. How can I prevent a slow leak in my bicycle tire?

To prevent a slow leak in your bicycle tire, it is important to regularly inspect and maintain your tires. This includes checking the tire pressure, looking for signs of wear and tear, and keeping the tires properly inflated. Avoid riding over rough terrain and be cautious of any potential hazards on the road, such as sharp objects.

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