Water flow along horizanta pipe at cross sectional area 48cm which has a constriction at cross sectional area 12cm at one place if the speed at the water at the constriction point is 4m/s calculate the speep at the wide section
To calculate the speed of water at the wide section of the pipe, we can use the principle of conservation of mass, which states that the mass of the water flowing through the pipe remains constant throughout.
The cross-sectional area of the pipe at the constriction is 12 cm², and the speed of water at the constriction point is 4 m/s. We can calculate the speed at the wide section using the formula:
A1 × v1 = A2 × v2
Where:
A1 = cross-sectional area at the constriction (12 cm²)
v1 = speed at the constriction point (4 m/s)
A2 = cross-sectional area at the wide section (48 cm²)
v2 = speed at the wide section (to be determined)
Converting the units:
12 cm² = 0.0012 m²
48 cm² = 0.0048 m²
Now, let's plug in the given values:
0.0012 m² × 4 m/s = 0.0048 m² × v2
Simplifying the equation:
0.0048 × v2 = 0.0012 × 4
0.0048 × v2 = 0.0048
Now, divide both sides by 0.0048:
v2 = 0.0048 / 0.0048
v2 = 1 m/s
Therefore, the speed of water at the wide section of the pipe is 1 m/s.