Answer:
a) 14.76 psi
b) 15.59 psi
c) 15.68 psi
d) The solution method is reasonable
Explanation:
The formula for maximum pressure is given as using Bernoulli's Equation :
Pmax = p + 1/2ρV²
Where ρ = Density = 0.002376slug per cubic foot
p = Atmospheric pressure in pounds per cubic foot = 14.6959 pounds per square inch
Converting pounds per square inch to pounds per square foot
= 1 pounds per square inch = 144 pounds per square foot
14.6959 pounds per square inch =
14.6959 pounds per square inch × 144 pounds per square foot
= 2116.2096 pounds per square foot
V = Velocity of the flow = Speed limit.
(a) For safety, the pit lane speed limit is 60 mph. At this speed, what is the maximum pressure on his hand?
Our speed limit is 60 mph
We convert to ft/s
1 mph = 1.46667 ft/s
60 mph =
60 mph × 1.46667 ft/s = 88 ft/s
Pmax = p + 1/2ρV²
Pmax = 2116.2096 + (0.5 × 0.002376 × 88²)
Pmax = = 2125.409472 Ib/ft² =
Converting to psi.
= 2125.409472/144
= 14.759788 psi
≈ 14.76 psi
(b) Back on the race track, what is the maximum pressure when he is driving his IndyCar at 225 mph?
Our speed limit is 225 mph
We convert to ft/s
1 mph = 1.46667 ft/s
225 mph =
225 mph × 1.46667 ft/s = 330 ft/s
Pmax = p + 1/2ρV²
Pmax = 2116.2096 + (0.5 × 0.002376 × 330²)
Pmax = 2245.5828 Ib/ft² =
Converting to psi.
= 2245.5828/144
= 15.594325 psi
≈ 15.59 psi
(c) On the straightaways, the IndyCar reaches speeds in excess of 235 mph.
Our speed limit is 235 mph
We convert to ft/s
1 mph = 1.46667 ft/s
235 mph =
235 mph × 1.46667 ft/s = 344.667 ft/s
Pmax = p + 1/2ρV²
Pmax = 2116.2096 + (0.5 × 0.002376 × 344.667²)
Pmax = = 2257.338465 Ib/ft² =
Converting to psi.
= 2257.3384654/144
= 15.675961562 psi
≈ 15.68 psi
d) For this speed, is your solution method for parts (a and (b) reasonable? Explain.
It is important to note that: the value of 1 atmosphere = 14.696 psi
If we look at the solution above, we can see that the maximum pressure of the speeds in question a, b, c which are: 14.76 psi, 15.59 psi, 15.68 psi respectfully are just a little bit outside the range of 1 atmosphere.
Hence, this is not significant enough to cause damage or harm the hands of Tony Kanaan therefore, my solution method for parts (a and (b) reasonable is reasonable.
