the velocity of water in a 4 cm diameter pipe is 2.0m/s.what is the velocity in a 2cm diameter pipe which connects with it,both pipes flowing full?

Area1*velocity1=area2*velocity2

looks like (4/2)^2 or 4 times the velocity.

To find the velocity in the 2 cm diameter pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate should be constant between two connected pipes.

The equation for mass flow rate (Q) is given by:

Q = ρ * A * V

where:
Q is the mass flow rate,
ρ is the density of the fluid (assumed to be constant),
A is the cross-sectional area of the pipe, and
V is the velocity of the fluid.

Now, let's calculate the cross-sectional areas of the two pipes.

For the 4 cm diameter pipe:
Radius (r1) = diameter / 2 = 4 cm / 2 = 2 cm = 0.02 m

Area (A1) = π * r1^2
= π * (0.02 m)^2

For the 2 cm diameter pipe:
Radius (r2) = diameter / 2 = 2 cm / 2 = 1 cm = 0.01 m

Area (A2) = π * r2^2
= π * (0.01 m)^2

Now, we know that the mass flow rate (Q) is the same for both pipes since they are connected and flowing full. Therefore:

Q1 = Q2

Using the formula for mass flow rate, we get:

ρ * A1 * V1 = ρ * A2 * V2

Since the density (ρ) is constant and cancels out, we can simplify the equation to:

A1 * V1 = A2 * V2

Now, we can substitute the known values into the equation:

π * (0.02 m)^2 * 2.0 m/s = π * (0.01 m)^2 * V2

Now we can solve for V2:

(0.04 π) * 2.0 = (0.01 π) * V2

0.08 = 0.01 V2

V2 = 0.08 / 0.01

V2 ≈ 8 m/s

Therefore, the velocity in the 2 cm diameter pipe is approximately 8 m/s.