Solving Perplexing Problems: 2 Examples

[tucky]

Perplexed again!

I have two problems that I am stuck on...I don’t even know if I am going about these correctly.

1. A fountain consists of water jets mounted so that their nozzles are 2 ft above a pool. Each jet squirts water out at a 45o angle. The water lands in the pool approximately 4 feet from the jet. The nozzle on the jet is 0.5 inch in diameter. There are eight of these jets in the fountain. At what rate must water be pumped through the fountain (in gallons/hour)?

4ft=1.219m, 2ft=.6096m
1.219m/ cos 45 = 1.7239m
1.7239 sin 45= 1.219

1.219+.6096=1.828m how far the water traveled

v^2=0+2*9.8m/s^2(1.8196-.6069)
v^2=4.88m/s

d=.0127m
A=pi(.0127m)^2
A=.0005067m^2

Av=Rvol=.00247m^3/s*4+.00989m^3/s=9404gall/hr

2.)A precise barometer can be constructed as shown at right. A tube full of some liquid is inverted in a pool of that liquid. The fluid settles into equilibrium, with a vacuum above the fluid. The height of the column of fluid indicates the atmospheric pressure.

Calculate what h will be for standard atmospheric pressure at sea level if the liquid in the barometer is Water

I know that I should use bernoulli’s equation
P1 + gy1 + ½v12 = P2 + gy2 + ½v22
v1=0 density=1000kg/m^3
y1=0 P1=101,300N/m^2
v2=0
y2=h

101,300N/m^2=P2+(1000kg/m^6)(9.8N)(h)

I have two variable (P2 and h) I do not know how to solve the rest? Can anyone help?

Thanks for your help in advance

 

[Doc Al]

Some hints:

For #1: What's the area of a circle?

For #2: You don't need the big guns of Bernoulli. This is a statics problem.

 

[M98Ranger]

For the first problem, you are on the right track with using the equation v^2=2gh to calculate the velocity of the water coming out of the jets. However, you also need to take into account the diameter of the nozzle and the fact that there are eight jets. This means that the total volume of water being pumped per second is 8 times the volume of water coming out of one jet. From there, you can convert the volume per second to gallons per hour.

For the second problem, you are correct in using Bernoulli's equation. However, you are missing the velocity term (v2) in your equation. You can use the fact that the fluid is in equilibrium to set the velocities at the top and bottom of the tube to be equal, and solve for the height (h) from there. Remember to also convert units to make sure they are all consistent.