# Water Velocity and Pressure From 5 degree Gradient At 200 m

1. Oct 28, 2015

### morrobay

1, Problem Statement.
A resevoir releases water into a 2 meter diameter drain pipe that is 200 m long with a 5ο gradient drop. Assume pipe is full without friction. If v0 is zero what is velocity at 200 meter discharge ?
And what is the pressure in atm ? The height at pipe end is - 17 meters. A 17 m drop from resevoir to end of 200 meter pipe

2. Relevant equations
For vertical time , y = 1/2 at2 = 1,86 sec
For vertical velocity vy = v = √2ay = 18m/sec
Pressure = Force/Area = mass*acc/area = 628000 kg * 9,8m/sec2/3.14 m2
Pressure = p0 + ρ h g
Assume water density = 1
3. The attempt at a solution
Sine 50 = .087. = 18m/s/v = 204m/sec ? or is it sine 50 (18m/s) = 1.5m/sec ?
Not sure about pressure formula to atm

All Im looking for are the equations for velocity and pressure at pipe exit from above data. http://www.calctool.org/CALC/eng/civil/hazen-williams_g

Last edited: Oct 28, 2015
2. Oct 28, 2015

### morrobay

Attempt # 2.
This is a velocity vector problem t0 v0 = 0 with theta 50 with x axis
v0x = v0 cos θ
v0y = v0 sin θ
vy = v0 sin θ +gt
The only component I can solve for is vy =√2gh == 18,25 m/sec
So I am missing a = ax + ay

3. Nov 1, 2015

### morrobay

The acceleration for this problem is g sin 50 and final velocity = v2 = 2(g *sin50 *200m) = 18.5 m/sec

Last edited: Nov 1, 2015
4. Nov 1, 2015

### billy_joule

Was a diagram provided? What pressure is it asking for?
For a problem like this it's generally safe to assume no acceleration occurs in the pipe, and pressures at the reservoir surface and pipe outlet are both atmospheric.

Are you familiar with Bernoulli's equation?

5. Nov 1, 2015

### morrobay

this should be solution
p = 1/2 ρv2 +ρ g h = constant But not familiar enough with crossover units in order to convert the above velocity , 18.5 m/sec, full 2 m diameter pipe to pressure in atmospheres at pipe outfall. I agree with assumptions above. The question is based on a submarine outfall about 17m below sea level from the 200m pipe that is gravity fed from reservoir on shore at sea level . At outfall the pressure in the ocean surroundings in atmospheres is p = p0 = ρgh about 2.7 atmospheres. So I want to know if outfall pressure from pipe is greater than 2.7 atmospheres. Otherwise a pump would be required for storm water drainage from reservoir.

Last edited: Nov 1, 2015
6. Nov 1, 2015

### billy_joule

If the reservoir surface is also at sea level then clearly no water would flow.
But, if my interpretation is correct, from the given information it can be found that the reservoir surface is slightly above sea level so there is a pressure difference so water will flow. Though, the question is a little ambiguous/contradictory on this point. Have you provided the question word for word?

I don't know what 'crossover units' are, you can use any units you like in the Bernoulli's, as long as you are consistent.

Why are you bringing up a pump? Is there more to the question statement?
If you want to know if the reservoir is free draining to the ocean all you have to look at is if sea level is lower than the reservoir level. That is all the information you need.

7. Nov 1, 2015