a pipe carrying 20degrees of water has a diameter 2.5cm.Estimate the maximum flow speed if the flow must be streamline?
bobpursley, you literally copy pasted Vader's answer from yahoo answers, really original working out lmao
To estimate the maximum flow speed for streamline flow in a pipe carrying 20 degrees water with a diameter of 2.5 cm, we can use the concept of laminar flow.
Laminar flow is characterized by smooth, layered flow with minimal disruptions or turbulent behavior. In order to determine the maximum flow speed, we can use the equation for the maximum flow rate in a circular pipe for laminar flow.
The equation for the maximum flow rate in laminar flow is given by:
Q = (pi * r^2 * deltaP) / (4 * eta * L)
Where:
Q = Maximum flow rate
pi = 3.14159
r = Radius of the pipe (half of the diameter)
deltaP = Pressure difference
eta = Dynamic viscosity of the fluid (for water at 20 degrees, it is approximately 0.001 kg/(m*s))
L = Length of the pipe segment
In this case, since we are interested in the maximum flow speed, we can convert the maximum flow rate to the maximum velocity (v) using the equation:
v = Q / (pi * r^2)
Let's calculate it step by step:
Step 1: Convert the diameter of the pipe to radius:
r = 2.5 cm / 2 = 1.25 cm = 0.0125 m
Step 2: Calculate the maximum flow rate (Q):
Assuming we have a pressure difference of 1 atm (which is approximately 101325 Pa), and let's assume a length of 1 meter for simplicity, we can substitute the values into the equation to calculate Q:
Q = (pi * (0.0125)^2 * 101325) / (4 * 0.001 * 1)
Q ≈ 1.23 x 10^(-4) m^3/s
Step 3: Calculate the maximum flow velocity (v):
v = (1.23 x 10^(-4) m^3/s) / (pi * (0.0125)^2)
v ≈ 0.785 m/s
Therefore, the estimated maximum flow speed for streamline flow in the given pipe carrying 20 degrees water with a diameter of 2.5 cm is approximately 0.785 m/s.
To estimate the maximum flow speed of water in a streamline flow through a pipe, we can use Bernoulli's principle. Bernoulli's principle states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume of a fluid remains constant along a streamline.
To calculate the maximum flow speed, we need to make some assumptions:
1. The flow is incompressible, meaning that the density of water remains constant.
2. The flow is steady, meaning that the velocity at any point in the pipe does not change over time.
3. The flow is fully developed, meaning that the velocity profile across the pipe is fully developed and consistent.
Now let's calculate the maximum flow speed step by step:
Step 1: Find the density of water.
The density of pure water at 20 degrees Celsius is approximately 998 kg/m^3.
Step 2: Convert the diameter from cm to m.
The diameter is given as 2.5 cm. We need to convert this to meters by dividing it by 100:
2.5 cm ÷ 100 = 0.025 meters.
Step 3: Calculate the cross-sectional area of the pipe.
The cross-sectional area of a pipe can be calculated using the formula:
Area = π × (radius)^2,
where the radius is half the diameter.
radius = 0.025 meters ÷ 2 = 0.0125 meters.
Area = π × (0.0125 meters)^2.
Step 4: Substitute values into Bernoulli's equation.
Bernoulli's equation for streamline flow in a pipe can be written as:
P + (1/2) ρ v^2 + ρgh = constant,
where P is the pressure, ρ is the density, v is the velocity, g is the acceleration due to gravity, and h is the height above a chosen reference point.
In this case, we assume that the height above the reference point and the change in pressure are negligible. Therefore, the equation simplifies to:
(1/2) ρ v^2 = constant.
Step 5: Solve for the maximum flow speed.
To find the maximum flow speed, we solve for v:
(1/2) ρ v^2 = constant,
v^2 = (2 × constant) / ρ,
v = √[(2 × constant) / ρ].
In this case, the constant is determined by the initial conditions of the flow and the shape of the pipe. For fully developed flow in a pipe, the constant can be approximated as 2.
Substituting the values, we get:
v = √[(2 × 2) / 998 kg/m^3].
Calculating this, we find the approximate maximum flow speed of water in the pipe to be:
v ≈ 0.063 m/s.
So, the estimated maximum flow speed for water in a streamline flow through the pipe is approximately 0.063 m/s.
20°C water ==> density = ρ = 1000 kg/m³
r = d/2 = 0.0165 m
A = 0.000855 m²
Q = ΔV/Δt
Q = volumetric flow rate
ΔV = change in volume flowing through the area
Δt = time interval of volumetric flow
Also:
Q = v · A = vA cos θ
v = velocity field of the substance elements flowing
A = cross-sectional vector area/surface
θ = 0 ==> cos θ = 1
v = Q/A = Q/0.000855