How Does Water Pressure Change with Velocity and Elevation in a Tapered Pipe?

AI Thread Summary
In a tapered pipe scenario, water speed increases from 0.90 m/s to 3.9 m/s as it rises to the second floor, while pressure decreases due to the combined effects of increased velocity and elevation. The initial pressure at the basement is 170 kPa, and using Bernoulli's equation, the pressure at the second floor can be calculated. The constant in Bernoulli's equation is determined by the conditions at the basement level where height is zero. After calculations, the pressure at the second floor is found to be approximately 88 kPa. This demonstrates the relationship between water pressure, velocity, and elevation in fluid dynamics.
bearhug
Messages
78
Reaction score
0
A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what is the (a) speed, and (b) water pressure, at the second floor?

the speed I got to be 3.9m/s now I'm having a hard time finding pressure.
I know that pressure decreases as velocity increased and as altitude increases, both of which are happening here. So I know that the pressure on the second floor is less than 170kPa. I'm trying to use Bernoulli's equation P + 1/2pv^2 + pgy=constant. First of all, what is the constant. My book doesn't explain this at all just has it appear in this equation. One way I approached the problem is by using the equation P1 - P2 = pgh and solving for P2 but I'm not sure if this is anywhere close to right. Any help is appreciated.
 
Physics news on Phys.org
bearhug said:
A water pipe having a 2.5 cm inside diameter carries water into the basement of a house at a speed of 0.90 m/s and a pressure of 170 kPa. If the pipe tapers to 1.2 cm and rises to the second floor 7.6 m above the input point, what is the (a) speed, and (b) water pressure, at the second floor?

the speed I got to be 3.9m/s now I'm having a hard time finding pressure.
I know that pressure decreases as velocity increased and as altitude increases, both of which are happening here. So I know that the pressure on the second floor is less than 170kPa. I'm trying to use Bernoulli's equation P + 1/2pv^2 + pgy=constant. First of all, what is the constant. My book doesn't explain this at all just has it appear in this equation. One way I approached the problem is by using the equation P1 - P2 = pgh and solving for P2 but I'm not sure if this is anywhere close to right. Any help is appreciated.

The constant is the value of the Bernoulli equation in the basement where h = 0.

But that does not give you the speed. The speed is determined by the rate of flow. Work out the speed on the second floor from the rate of flow. Then put that speed in the Bernoulli equation along with the height to determine the pressure on the second floor.

AM
 
I already have the speed. 3.9m/s and I'm using the density of freshwater being 1.0e3 kg/m^3. I know I'm calculating something wrong I keep coming up with a huge number or a negative number for pressure which, can't be negative right? and needs to be less than 170 kPa.
 
bearhug said:
I already have the speed. 3.9m/s and I'm using the density of freshwater being 1.0e3 kg/m^3. I know I'm calculating something wrong I keep coming up with a huge number or a negative number for pressure which, can't be negative right? and needs to be less than 170 kPa.

I get about 88 kPa for the pressure. The pressure in SI units is 170000 N/m^2 or Pa.

AM
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

What is the Pressure Change in a Pipe for Salt Water Transport?
Replies
5
Views
2K
Pressure change in pipe due to sudden closure of valve
Replies
1
Views
2K
Bernoulli equation / fluid flow / finding height
Replies
6
Views
3K
How Does Bernoulli's Principle Apply to Varying Pipe Diameters and Water Flow?
Replies
3
Views
2K
Finding speed of water leaving a pressurized vessel
Replies
1
Views
9K
Solving Water Flow in a Taper Pipe Problem
Replies
1
Views
2K
Water Velocity and Pressure From 5 degree Gradient At 200 m
Replies
6
Views
2K
Solve Bernoulli's Equation for Water Height Rise
Replies
14
Views
2K
Calculate the rate of potential energy loss of water in a pipe
Replies
2
Views
2K
Bernoulli's equation/pressure question
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top