Fluids- Pressure and Flow Measurement Flashcards
How does a manometer work?
Has two tubes coming out above a flow though a pipe. The fluid level in these tubes can be used to find pressure at there positions along the flow. Uses equation Pi=ρghi where hi is vertical distance between fluid level in tube to centre line of flow.
What is static pressure?
Represents the actual thermodynamic pressure of the fluid. Used in thermodynamic property tables
What is dynamic pressure?
Represents the pressure rise when the fluid motion is brought to a stop isentropically
What is hydrostatic pressure?
The pressure calculated by ρgh
What is stagnation pressure?
Sum of static and dynamic pressure
How is a U-tube manometer set up?
Has tube going down from one position earlier in the flow going vertically down, then diagonal. Then there is a U shape which contains the manometer fluid which is more dense than the fluid in the pipe.
How to do calculations with a U-tube manometer
The manometer fluid will be lower down on left in the U. Manometer fluid is in equilibrium so pressure at position where it starts on the left is same as same level on the right. The pressure at the start of the tube (1) plus ρ1g(a+h) equals pressure where tube rejoins (2) plus ρ1ga+ρ2gh. Where a is vertical distance from tube to start of manometer fluid on right. h is vertical distance between top levels of manometer fluid on each side of U.
Apply Bernoulli’s equation to a streamline that ends at a point on an object
Final velocity is 0 and height doesn’t change
P1/ρg+C1^2/2g=P2/ρg
If we can measure P2 and P1 we can get free steam velocity C1
How can a pitot tube and static tube be used to find free stream velocity?
Put normal static tube vertically above where pitot tube starts. The height of fluid in static tube corresponds to just static pressure. Use Bernoulli on streamline that ends at stagnation point to get
C1=rt(2ΔP/ρ). Can then feed the tubes into a differential manometer to find difference in pressure. Sub this in to get
C=rt(2gh(ρ2/ρ-1))
What does a pitot tube look like and do?
Usually a right angled tube that starts parallel to flow (in the tube) and then goes out of the tube. There is a stagnation point where the fluid enters the tube. The height the fluid gets to corresponds to the stagnation pressure.
What does a pitot-static tube look like?
Looks like a pitot tube but around it is a static head tube (at same right angle). There is an inlet into the total head tube where the stagnation point is. There are static holes to allow fluid into the static head tube (>2). Position of these holes is known.
Positives and negatives of pitot-static tube
BS devices give 1% error. Can be made very small. Cheap, robust, simple, accurate, close to point measurement.
But has slow response.
What does a Venturi meter look like?
Fluid flows into convergent section (nozzle) which has φ of at least 20. Takes it to the throat. Then diffuser back to normal diameter (φ about 6). It has a U-tube manometer arrangement from just before the nozzle to the throat. Just before nozzle is position 1, throat is position 2.
Formula for flow rate using Venturi meter
Q=A1C1
Q=A1rt(2ΔP/ρ((A1/A2)^2-1))
This substitution for C1 comes from Bernoulli where Δz=0 and C is rewritten in terms of Q and A
Why is the flow rate calculated from a Venturi meter an overestimate and how do you correct it?
Pressure drop measured not just due to increase in velocity but also minor pressure losses associated with geometry.
Multiply measure Q by Cd (discharge coefficient) which is always less than 1. For Re>30,000 Cd can be taken as 0.96
