1. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex1 ]
GIVEN:
We know the water flows from the 1st floor with a velocity of 20 fps.
REQD:
Given the velocity and geometry in the figure, use Bernoulli equation to solve for the maximum water velocity in the basement and on the 2nd floor.
Fluid Mechanics and Hydraulics

2. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex1 (cont’d) ]
SOLU:
1. Let’s write the BE between (1) and (2)
- (1)
2. Let’s plug in some numbers and solve for V2
thus
Fluid Mechanics and Hydraulics

3. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex1 (cont’d) ]
SOLU:
3. Now write the BE between (1) and (3)
- (2)
4. Let’s plug in some numbers and solve for V3
- (3)
thus 
WHAT?
this is impossible, so we know that no flow comes out on second floor at current supply pressure
Fluid Mechanics and Hydraulics

4. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex2 ]
GIVEN:
This firehose with the illustrated geometry must be able to deliver 250 GPM
REQD:
What upstream pressure must we supply to provide the required flow rate?
SOLU:
1. Let’s write the BE between (1) and (2)
- (E1)
2. Convert Q in GPM to Q in fps
Fluid Mechanics and Hydraulics

5. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex2 (cont’d) ]
SOLU:
3. And we know we can get V2 and V1 from continuity
- (E2)
- (E3)
4. Now we sub (E2) and (E3) into (E1) to get
- (E4)
Fluid Mechanics and Hydraulics

6. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex2 (cont’d) ]
SOLU: or
- (ans)
Fluid Mechanics and Hydraulics

7. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex3 ]
GIVEN:
REQD:
In this inviscid flow, determine the diameter of the outlet at the free jet required to establish an exit velocity of 20 fps
SOLU:
1. Let’s write the BE between (1) and (2)
- (E1)
2. Drop-in what we know
- (E2)
Fluid Mechanics and Hydraulics

8. THE BERNOULLI EQUATION: FURTHER APPLICATION
[ additional examples: ex3 (cont’d) ]
SOLU:
3. Solving we find
- (E3)
4. Then, enforcing continuity we arrive at
- (E4)
- (E5)
Fluid Mechanics and Hydraulics