2.50 Consider the following message: FORMULA FOR SUCCESS (a) Estimate the probabilities of the letters in the message using the
1 answer:
Answer:
Part a: The probability of each letter is given in the table below.
Part b: The average information in this message is 1.91.
Explanation:
Part a:
The message is given as
FORMULA FOR SUCCESS
Total number is given as n=17
Letter x Probability p(x)
F 2 2/17
O 2 2/17
R 2 2/17
M 1 1/17
U 2 2/17
L 1 1/17
A 1 1/17
S 3 3/17
C 2 2/17
E 1 1/17
Part b
The information is given as
Letter x Probability p(x) xp(x)
F 2 2/17 4/17
O 2 2/17 4/17
R 2 2/17 4/17
M 1 1/17 1/17
U 2 2/17 4/17
L 1 1/17 1/17
A 1 1/17 1/17
S 3 3/17 9/17
C 2 2/17 4/17
E 1 1/17 1/17
______________________________________
Total 1.91
So the average information in this message is 1.91.
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Answer:
a) The maximum flowrate of the pump is approximately 13,305.22 cm³/s
b) The pressure difference across the pump is approximately 293.118 kPa
Explanation:
The efficiency of the pump = 78%
The power of the pump = 5 -kW
The height of the pool above the underground water, h = 30 m
The diameter of the pipe on the intake side = 7 cm
The diameter of the pipe on the discharge side = 5 cm
a) The maximum flowrate of the pump is given as follows;
Where;
P = The power of the pump
Q = The flowrate of the pump
ρ = The density of the fluid = 997 kg/m³
h = The head of the pump = 30 m
g = The acceleration due to gravity ≈ 9.8 m/s²
= The efficiency of the pump = 78%
= 5,000 × 0.78/(997 × 9.8 × 30) ≈ 0.0133 m³/s
The maximum flowrate of the pump ≈ 0.013305 m³/s = 13,305.22 cm³/s
b) The pressure difference across the pump, ΔP = ρ·g·h
∴ ΔP = 997 kg/m³ × 9.8 m/s² × 30 m = 293.118 kPa
The pressure difference across the pump, ΔP ≈ 293.118 kPa