Pressure at the closed end of a pipe with a leak?

[Austin J]

Suppose I have an air pipe that is used for "grasping" other objects using negative pressure. When an object is grasped, assume it is a perfect seal and that end of the pipe is closed. On the other end of the pipe is the pressure source creating the vacuum. Somewhere in the middle is a short, smaller arm of the pipe that is open to the air. This serves as a leak.

1.) It is my understanding that there is a linear pressure drop from the source to the leak, and that the pressure between the leak and the closed end of the pipe is constant. Is this correct?

2.) What is the relationship between the grasping pressure (i.e. the pressure at the closed end of the pipe) and the area of the leak pipe? I would like to express the pressure at the closed end of the pipe as a function of the area of the leak pipe.

 

[Bystander]

Suppose I have an air pipe that is used for "grasping" other objects using negative pressure. When an object is grasped, assume it is a perfect seal and that end of the pipe is closed. On the other end of the pipe is the pressure source creating the vacuum. Somewhere in the middle is a short, smaller arm of the pipe that is open to the air. This serves as a leak.
1.) It is my understanding that there is a linear pressure drop from the source to the leak, and that the pressure between the leak and the closed end of the pipe is constant. Is this correct?

Within the framework of the question, "Yes."

2.) What is the relationship between the grasping pressure (i.e. the pressure at the closed end of the pipe) and the area of the leak pipe? I would like to express the pressure at the closed end of the pipe as a function of the area of the leak pipe bleed rate is a function of area, length , and ... who knows.