1. Student uses a laser Doppler velocity meter to measure the free stream velocity of a water channel in the fluids lab. Her 12 readings are: V =1.15, 1.23. 1.18, 1.19, 1.14, 1.21, 1.19, 1.26, 1.20, 1.15, 1.16, and 1.17 m/s. (a) Calculate the mean, deviation, and sample standard deviation of this set of measurements. Be sure to include units in your answers. (b) Plot a histogram of these data. 2. Perform a least-squares fit (linear regression analysis) on the following six (x.y) data pairs: (0,2.4), (2.9.5), (4,7.5), (6,16.9), (8,14.3), and (10,19.4). Calculate the lincar correlation coefficient (ry), the slope (a), and the y intercept (b) of the best-fit straight line. Plot the data points as symbols (no line) and the line as a solid line (no symbols) for comparison. To what level of confidence can you say there is a trend? 3. A micrometer of unknown origin is used to measure the diameter of a steel rod that is known to have a diameter of 0.5000 in. You use the micrometer to make 10 independent measurements of the rod diameter, and the results are: 0.4821,
1. Student uses a laser Doppler velocity meter to measure the free stream velocity of a water channel in the fluids lab. Her 12 readings are: V =1.15, 1.23. 1.18, 1.19, 1.14, 1.21, 1.19, 1.26, 1.20, 1.15, 1.16, and 1.17 m/s. (a) Calculate the mean, deviation, and sample standard deviation of this set of measurements. Be sure to include units in your answers. (b) Plot a histogram of these data. 2. Perform a least-squares fit (linear regression analysis) on the following six (x.y) data pairs: (0,2.4), (2.9.5), (4,7.5), (6,16.9), (8,14.3), and (10,19.4). Calculate the lincar correlation coefficient (ry), the slope (a), and the y intercept (b) of the best-fit straight line. Plot the data points as symbols (no line) and the line as a solid line (no symbols) for comparison. To what level of confidence can you say there is a trend? 3. A micrometer of unknown origin is used to measure the diameter of a steel rod that is known to have a diameter of 0.5000 in. You use the micrometer to make 10 independent measurements of the rod diameter, and the results are: 0.4821,
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Transcribed Image Text:1. Student uses a laser Doppler velocity meter to measure the free stream velocity of a
water channel in the fluids lab. Her 12 readings are:
V = 1.15, 1.23, 1.18, 1.19, 1.14, 1.21, 1.19, 1.26, 1.20, 1.15, 1.16, and 1.17 m/s.
(a) Calculate the mean, deviation, and sample standard deviation of this set of
measurements. Be sure to include units in your answers.
(b) Plot a histogram of these data.
2. Perform a least-squares fit (linear regression analysis) on the following six (x.y)
data pairs: (0,2.4), (2,9.5), (4,7.5), (6,16.9). (8,14.3), and (10,19.4).
Calculate the linear correlation coefficient (rxy), the slope (a), and the y intercept
(b) of the best-fit straight line. Plot the data points as symbols (no line) and the
line as a solid line (no symbols) for comparison. To what level of confidence can
you say there is a trend?
3. A micrometer of unknown origin is used to measure the diameter of a steel rod
that is known to have a diameter of 0.5000 in. You use the micrometer to make 10
independent measurements of the rod diameter, and the results are: 0.4821,
0,4824, 0.4821, 0.4820, 0.4822, 0.4821, 0.4822, 0.4820 and 0.4822. Estimate the
bias, precision and accuracy errors in these measurements.
4. A student measures the radius of a circle, i.e. R = 1.34 +/-0.040 cm, following
the two sigma or 95% confidence level standard. This represents a relative
uncertainty of +/-0.040/1.34 = +/-3.0%. He then calculates the area of the circle.
He reasons that the area will have the same relative uncertainty as the radius
measurement since there is only one independent variable in the equation, so he
reports his area as A = 5.64 +H- 0.17 cm?. But his answer is incorrect! Write the
correct area in standard engineering form, i.e. A =_+/-_ cm?.
5.The well-known Bernoulli equation is used to calculate the Bernoulli constant C
in a flow,
where P is the pressure, ñ is the fluid density, V is the magnitude of the velocity, g
is the gravitational constant, and z is the elevation. In a water flow experiment (p =
1000. kg/m3), the following measurements are made:
P= 20.5 +/-0.5 kPa,
V= 15.0 +/- 0.15 m/s.
and
2= 3.42 +/- 0.01 m
The gravitational constant is 9.81 m/s?. Calculate the RSS uncertainty for the
Bernoulli constant C, and write C in standard engineering notation (C =
+/-
m/s). Show all units for full credit.
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