- #1
squires80
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Hi all I'm trying to teach myself a bit of bernoulli's principle but i am struggling.
I'm pretty sure I need to use a combination of bernies equation and continuity equation but I get lost when trying to rearrange to find velocity.
Water moves through a constricted pipe in steady, ideal
flow. At the lower point, the pressure
is P1 17500 Pa and the pipe diameter is 6.00 cm.
At another point y 0.250 m higher, the pressure is P2 12000 Pa and the pipe diameter is 3.00 cm. Find the speed of flow (a) in the lower section and (b) in the upper
section. (c) Find the volume flow rate through the pipe.
P1/ρg+v^2/2g+y1 = P2/ρg+v^2/2g+y2
A1v1=A2v2
Information I have is
P1= 17500 Pa
P2= 12000 Pa
Y1= 0
Y2= 0.25m
A1= 0.0028 m2
A2= 0.00071 m2
I need to find v1 and v2 and volume flow rate
I know buy using the the continuity equation I can substitute the valve of v1 for v2,
but when I come to rearranging the formula it becomes a mess. I have searched online but lots of examples tend to skip important steps and just show the final equation.
I would like to know step by step how to do it. (please note that it has been nearly 20 years since I last did maths )
I'm pretty sure I need to use a combination of bernies equation and continuity equation but I get lost when trying to rearrange to find velocity.
Water moves through a constricted pipe in steady, ideal
flow. At the lower point, the pressure
is P1 17500 Pa and the pipe diameter is 6.00 cm.
At another point y 0.250 m higher, the pressure is P2 12000 Pa and the pipe diameter is 3.00 cm. Find the speed of flow (a) in the lower section and (b) in the upper
section. (c) Find the volume flow rate through the pipe.
Homework Equations
P1/ρg+v^2/2g+y1 = P2/ρg+v^2/2g+y2
A1v1=A2v2
The Attempt at a Solution
Information I have is
P1= 17500 Pa
P2= 12000 Pa
Y1= 0
Y2= 0.25m
A1= 0.0028 m2
A2= 0.00071 m2
I need to find v1 and v2 and volume flow rate
I know buy using the the continuity equation I can substitute the valve of v1 for v2,
but when I come to rearranging the formula it becomes a mess. I have searched online but lots of examples tend to skip important steps and just show the final equation.
I would like to know step by step how to do it. (please note that it has been nearly 20 years since I last did maths )
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