First Test Spring 2015 Hydraulic Engineering - Key
Full Name ______(100/110)
Closed book, two pages of notes one side in your own handwriting.
You must show the work for all problems to get credit.
Casio: All fx-115 models.
Hewlett Packard: The HP 33s and HP 35s models, but no others.
Texas Instruments: All TI-30X and TI-36X models.
By my signature below, I hereby swear that I have neither received aid from any other student, nor have I given aid to any other student on this exam.Moreover, I swear that I have not committed any form of academic dishonesty and have maintained ethical integrity in accordance with the UTEP Handbook of Operating Procedures, the UTEP Civil Engineering Honor Code, and the ASCE Code of Ethics.
Signature: ______
By my signature below, I swear that I have not witnessed any other student commit any form of academic dishonesty with regard to this exam.
Signature: ______
- (20) Mark the direction of flow. Rank the absolute value of velocity of the four systems, ignore minor losses. Write out the energy equation for systems A and C; show your points 1 and 2 on the figures; solve the energy equation for the velocity in both systems A and C.
Direction (4 pts, one for each system) all flow left to right
Magnitude A-8, D-5, C-2, b-2 6 pts, partial credit, 2 points for A first and 2 points for C=B
Equation, 5 pts each, 2 pt for points 1 and 2 both in correct locations; 3 pts for equation solution
A: V = sqrt( 2 g * 8 units/(fL/D+1))
C: V = sqrt(2 g 2 units/(fL/D))
2. (30) A 6 cm diameter smooth pipe 160 m long conveys 36 m3/hour (0.01 m3/s) of water at 25 degrees C from a sidewalk hydrant to the top of a building 25 m tall. What pressure can be maintained at the top of the building, if the hydrant pressure is 1.6 MPa? Note: both pressures are in the pipe.
What is the velocity?
a)(3) V = Q/A = 0.01/(3.14*0.062/4) = 3.537 m/s
b) (3) What is the Reynolds number?Re = D V/v = 0.060*3.537/(8.93 10-7) = 2.38 105
c) (3) What is the absolute or dynamic viscosity?
Absolute viscosity from table is: 8.9 10-4 N s/m2 but we typically use the kinematic viscosity in the Reynolds number
d) (3) What is the friction factor (show work on Moody diagram above)?
From Moody diagram for smooth pipes: f = 0.0145, allow 0.014 – 0.0155
e) (6) What is the head loss? (note: for (e) and (g) assume the friction factor is 0.018)
Head loss = V2/(2g )(f L/D) = 30.6 m
f) (6) Solve the energy equation for the upper pressure. Don’t use any numbers except where terms are zero or cancel
P2/(rho g) = P1/(rho g) + z1 – z2 – hloss note: velocity heads cancel
P2 = (P1/(rho g) + z1 – z2 – hloss )*(rho g)
g) (6) What is the pressure at the other end of the pipe? (note: for (e) and (g) assume the friction factor is 0.018)
P2 = (P1/(rho g) + z1 – z2 – hloss)*(rho g) = (163.09m + 0 – 25 m – 30.6m )*(rho g) = 1.05 *10^6 sPa = 1.05 MPa
3. (20) A 50 cm x 50 cm x 10 cm slab of epoxy coated concrete with a density of 3,000 kg/m3 is placed in a shallow pond with a depth of 2m. Find:
(5) Force of buoyancy in Newtons:
Weight of displaced water, volume = 0.5*0.5*0.1 = 0.025 m3, weight = 1000 kg/m3*9.81 m/s2*0.025 m3 = 245.25 N
(5) Force of Gravity in Newtons:
0.5*0.5*0.1*3000*9.81 = 735.75 N
(10) Show a free body diagram and include any other major forces not mentioned above (in Newtons)
It sits on the bottom and the bottom pushes up by
735.75-245.25= 495 N ½ credit for proper diagram with no numbers
4. ( 25) A semi-circular channel with a Manning' s n = 0.015, and a slope of 0.006 is 6.2 meters wide at the top and is flowing full. If the flow in the channel is 37.9 m3/s, is the flow sub or supercritical?
(5) Velocity = Q/A = 37.9/15.1 = 2.51 m/s
(5) Depth = width/2 = 6.2/2 = 3.1
(5) Hydraulic Radius = A/P = r/2 = 3.1/2 = 1.55
(5) Froude Number = V/sqrt(g A/T) = 2.51/sqrt(9.81*15.1/6.2) = 0.51
(5) Sub/Supercritical = Fr<1, subcritical give credit based on what they got for Fr
5. (15)
Label the flow transitions (two on in each figure (8). Circle any location(s) where flow is supercritical (4). Put a dashed circle around any location(s) where the Froude number = 1 (3).