Wk10 - Momentum

Question 1

How can the momentum equation for hydraulic systems be derived from the original momentum equation?

Answer 1

F=M/t (v2-v1)

M/t = pQ

F = pQ (v2-v1)

Q=A.V

F = p.A.V(v2-v1)

Question 2

What are the three scenarios resulting in a change in momentum?

Answer 2

Change in fluid velocity, direction, or both

Question 3

What is the formula for the sum of ‘Fx’

Answer 3

Sum Fx = pQ (v2x -v1x)

Fx = sum of external forces in x direction
p = density of water (1000kg/m3)
Q = discharge (m3/s)
v2x = velocity 2 in x direction
v1x = velocity 1 in x direction

Question 4

What is the formula for the sum of ‘Fy’

Answer 4

Sum Fy = pQ (v2y -v1y)

Fy = sum of external forces in y direction
p = density of water (1000kg/m3)
Q = discharge (m3/s)
v2y = velocity 2 in y direction
v1y = velocity 1 in y direction

Question 5

What assumptions must be made when considering momentum questions?

Answer 5

• That there is no turbulence in bends
• That there is no loss of momentum

Question 6

What does the sum of forces in the x direction, Fx, equation become?

Answer 6

P1A1 - P2A2.Cos(theta) - Frx

Sum of Fx = pQ(v2x-v1x)

becomes

pQ(v2.Cos(theta)-v1)

Question 7

What does the sum of forces in the y direction, Fy, equation become?

Answer 7

Fry - P2A2.Sin(theta)

Sum of Fy = pQ(v2y-v1y)

becomes

pQ(v2.Sin(theta))

Question 8

How is the resultant force calculated?

Answer 8

Fr = Root (Frx^2 + Fry^2)

Question 9

How is the resultant angle calculated?

Answer 9

Theta = Tan^-1 (Fry/Frx)

Question 10

How do you know which axis are positive?

Answer 10

The axis are positive in the initial direction of the fluid as it enters the control volume.

Question 11

What are the general steps to calculate the resultant force, Fr, in momentum questions? (6)

Answer 11

1. Draw control volume and external forces
2. Calculate algebraic sum of external forces
3. Equate sum of Fx to rate of change of momentum in x direction
4. Solve for Frx
5. Repeat for Fry
6. Calculate Fr and theta

Question 12

How do you calculate the velocity of the fluid at points 1 and 2?

Answer 12

V1 = Q/A1
V2 = Q/A2

A = Pi.Dia^2/4

Question 13

What does bernoulli’s equation become, and why?

Answer 13

• z1=z2=0
• g is eliminated
• IF P2 is atmospheric then P2=0

P1/p + v1^2/2 = P2/p + v2^2/2

Question 14

How is the modified bernoulli’s equation rearranged to solve for P2?

Answer 14

V1^2/2 - V2^2/2 = P2/p -P1/p

P2/p = V1^2/2 - v2^2/2 + P1/p

P2 = p(v1^2-v2^2)/2 + P1

Question 15

What do you rearrange Bernoulli’s equation to solve for, in a hose question?

Answer 15

P1

(P2=0)

Question 16

How are the LHS (left hand side) external forces summed up in the application of momentum to the x-direction?

Answer 16

Pressure force at 1 - (Pressure force at 2 x Cos(theta) - FrX

Where:
Pressure force at 1 = P1A1
Pressure force at 2 = P2A2

Question 17

How are the RHS (right hand side) external forces summed up in the application of momentum to the x-direction?

Answer 17

pQ(v2.Cos(theta)-v1)

Question 18

How are the external forces summed up in the application of momentum to the y-direction?

Answer 18

Sum of Fy

-P2A2.Sin(theta) + Fry
=
pQ(v2.Sin(theta))

Question 19

How is P1/P2 calculated if a pressure is given in the question, in meters.

Answer 19

P = pgh
p = density
g = gravity
h = height of pressure

Question 20

How do you calculate ‘p1’ if the pressure in the question is provided in terms of meters

e.g. the pressure at the bend is 30m of water.

Answer 20

p1 = pgh

= 1000x 9.81 x 30m