The friction velocity F of water flowing through a pipe is given by where g is the acceleration due to gravity, d is the diameter of the pipe, l is the length of the pipe, and h is the head loss. Estimate F, and find the uncertainty in the estimate, assuming that g = 9.80 m/s2 exactly, and that

a. d = 0.15 m and l = 30.0 m, both with negligible uncertainty, and h = 5.33 ± 0.02 m.

b. h = 5.33 m and l = 30.0 m, both with negligible uncertainty, and d = 0.15 ± 0.03 m.

c. d = 0.15 m and h = 5.33 m, both with negligible uncertainty, and l = 30.00 ± 0.04 m.

Answer :

Step 1 of 4 :

Given,

The friction velocity F of water flowing through a pipe is given by F = .

Where, g = acceleration due to gravity,

d = diameter of the pipe and

h = head loss.

The goal of the problem is

Given, d = 0.15 cm and l = 30.0 m, both with negligible uncertainty and h = 5.330.02mg = 9.80 m/

We have to find the estimate of F and the uncertainty in the estimate

b) Given, h = 5.33 cm and l = 30.0 m, both with negligible uncertainty and d = 0.150.03m

g = 9.80 m/

We have to find the estimate of F and the uncertainty in the estimate

c) Given, d = 0.15 cm and h=5.33m, both with negligible uncertainty and l = 30.000.04m

g = 9.80 m/

We have to find the estimate of F and the uncertainty in the estimate.

Step 2 of 4 :

The claim is to find the estimate of F and the uncertainty in the estimateGiven, d = 0.15 cm and l = 30.0 m, both with negligible uncertainty and h = 5.330.02m

g = 9.80 m/

Where, = 0.02 and h = 5.33

We have, F =

F =

= 0.2555

Then we have to find

=

Therefore =

= 0.110680

Thus, =

Then = 0.110680(

= 0.02397

Therefore, =

Where, = 0.02

= (0.02397) ( 0.02)

= 0.000479 0.0005

Hence, estimate of F is 0.2555 and the uncertainty in the estimate is

0.25550.0005 m/s.