 # Questions Regarding Fluid Mechanics

I had a recent homework assignment in my biofluid mechanics course, and I still don’t understand this one problem. I just don’t see what steps need to be taken in order to get the answer. Here’s the problem:

Water is in a pop bottle, with two holes in it. The depth of the two holes are h1 and h2. Assuming the holes are alligned perpendicular to the ground, the streams of water will meet at a certain horizontal distance away from the bottle, which we’ll call L. Show that L = 2*(h1*h2)^(1/2)

I also am having problems with my current assignment, which I know you guys aren’t supposed to help with, but perhaps you could point me in the right direction. The problem is:

A person holds her hand out of an open car window while the car drives through still air at 65mph. Under standard atmospheric conditions, what is the maximum pressure on her hand? What would be the maximum pressure if the “car” was an Indy 500 racer traveling at 220mph.

My work so far:
Assuming that a short distance in front of her hand, the air travels 65mph, and directly in front of her hand (right in front) there is a stagnation point, I used the Bernoulli Equation, saying:

P2 - P1 = 1/2pV1^2

(the z terms cancel because the two points are at the same height and the second velocity is zero, so that term is gone as well). The problem may lie in my conversion factors, converting from air density in slugs/ft^3 to lb/ft^3 and mph to ft/s (I do need to do that, right?). I ended up saying:

P2 - P1 = 1/22.3810^-3 slugs/ft^3 * 32 lb/slug * 65 mph * 5280ft/3600 sec. I get a pressure difference of 3.63 lb/ft^2, but the answer is supposed to be 10.8 lb/ft^2. Do I need to add standard atmosphere to this, and if so, how do I figure that out?

A couple hints:

Question 1: If I understand correctly, the two holes are one above another, oriented so that the water shoots out of the bottle parallel to the ground. What is the shape of the trajectory of the stream of water? How fast is it initially going when it leaves the bottle? Once you know these two things you should be able to solve for the intersection point.

Question 2: You’re on the right track. There are two errors in your calculation, though. For one, you forgot to square V1 when plugging in your numbers. For the other error, I’ll just give a hint: check your units carefully.