The static pressure in horizontal pipeline is 43000Pa and the cross sectional area is 20cm. The fluid is said to be incompressible and non viscous and has density of 1000kg/m. Calculate:-
-velocity
-The volume flow rate in a pipe
To calculate the velocity of the fluid in the pipeline, we can use the Bernoulli's equation, which relates the pressure, density, and velocity of a fluid.
Bernoulli's equation: P + (1/2)ρv^2 = constant
Where:
P = static pressure
ρ = density of the fluid
v = velocity of the fluid
Given data:
Static pressure (P) = 43000 Pa
Density (ρ) = 1000 kg/m^3
Let's calculate the velocity:
P + (1/2)ρv^2 = constant
Let's assume the constant to be C.
Therefore,
C = P + (1/2)ρv^2
Now, let's solve for v:
(1/2)ρv^2 = C - P
v^2 = 2*(C - P)/ρ
v = √(2*(C - P)/ρ)
Since we have the density (ρ) given, we can substitute the values into the equation to find v.
Now, to calculate the volume flow rate in the pipe, we can use the formula:
Q = Av
Where:
Q = volume flow rate
A = cross-sectional area of the pipe
v = velocity of the fluid (calculated above)
Given data:
Cross-sectional area (A) = 20 cm^2
Let's calculate the volume flow rate:
Q = Av
Since we are given the area in cm^2, let's convert it to m^2:
20 cm^2 = 20/10000 m^2 = 0.002 m^2
Now, substitute the values into the equation to find Q.
Please provide me with the value of the constant (C) in order to calculate the velocity.
To calculate the velocity of the fluid in the horizontal pipeline, we can use the equation:
velocity (v) = √(2 * (static pressure (P) / density (ρ)))
First, convert the cross-sectional area from cm² to m².
Given that the cross-sectional area (A) is 20 cm², we can convert it to m² using the conversion factor 1 m² = 10,000 cm²:
A = 20 cm² * (1 m² / 10,000 cm²) = 0.002 m²
Next, plug in the values into the equation:
v = √(2 * (43,000 Pa / 1,000 kg/m³))
= √(2 * 43 m²/s²)
≈ √(86) m/s
≈ 9.28 m/s
Therefore, the velocity of the fluid in the horizontal pipeline is approximately 9.28 m/s.
To calculate the volume flow rate in the pipe, we can use the equation:
volume flow rate (Q) = velocity (v) * cross-sectional area (A)
Given that the velocity (v) is 9.28 m/s and the cross-sectional area (A) is 0.002 m², we can calculate the volume flow rate (Q):
Q = 9.28 m/s * 0.002 m²
= 0.01856 m³/s
Therefore, the volume flow rate in the pipe is approximately 0.01856 m³/s.