Diameter =.2mm
Length=200 mm
HL=2.75 m
Viscosity = 1.5 x10^-6 m^2/s
Find: Reynolds number and velocity in the pipe
To find the Reynolds number and velocity in the pipe, you can use the following equations:
Reynolds Number (Re) = (Velocity × Diameter) / Viscosity
Velocity (V) = (Re × Viscosity) / Diameter
First, let's find the Reynolds number:
1. Determine the velocity (V) in the pipe using the given data.
- No data is provided for the velocity, so we need to find it first.
- To find the velocity, we can use Torricelli's Law, which states that the velocity of a fluid exiting a small hole is given by the equation:
V = √((2 × g × d))/((1 - (A/A0))× C)
- Here, g is the acceleration due to gravity (approximately 9.8 m/s^2).
- d is the depth of the hole, which is equal to the length of the pipe (200 mm = 0.2 m in this case).
- A is the cross-sectional area of the hole.
- A0 is the cross-sectional area of the pipe.
- C is the coefficient of discharge. As a general assumption, we can assume it to be 1.
- Plugging in the values, we get:
V = √((2 × 9.8 × 0.2))/((1 - (A/A0))× 1)
2. Calculate the cross-sectional area of the hole (A):
- The hole is given by the diameter (0.2 mm).
- The cross-sectional area can be calculated using the formula:
A = π × (Diameter/2)^2
- Plugging in the values, we get:
A = π × (0.2/2)^2
3. Calculate the cross-sectional area of the pipe (A0):
- The diameter of the pipe is given as 0.2 mm.
- The cross-sectional area can be calculated using the formula:
A0 = π × (Diameter/2)^2
- Plugging in the values, we get:
A0 = π × (0.2/2)^2
4. Calculate the velocity using the obtained values of A, A0, and V from steps 2 and 3 in the Torricelli's Law equation.
Now that we have the velocity (V), we can find the Reynolds number (Re) using the provided data:
Re = (Velocity × Diameter) / Viscosity
Plugging in the values of V, Diameter (0.2 mm = 0.0002 m), and Viscosity (1.5 x 10^-6 m^2/s), we can calculate the Reynolds number.
Finally, we will have both the Reynolds number and the velocity in the pipe.