Linear InterpolationHomework Review

1. Estimate the viscosity of water at 55oF

(x1, y1) --> (50, 1.310)(x2, y2) -->(55, ?)(x3, y3) --> (60, 1.129)

2. Estimate the viscosity of water at 142oF

(x1, y1) --> (140, 0.470)(x2, y2) --> (142, ?)(x3, y3) --> (160, 0.401)

3. What is the difference in viscosity of 155oF water and 55oF water?... Know 55oF is 1.220cP from problem 1

(x1, y1) --> (140, 0.470)(x2, y2) --> (155, ?)(x3, y3) --> (160, 0.401)

1.220 – 0.418 = 0.802 cP

4. At what temperature is the viscosity of water 1cP?

(x1, y1) -->(1.129, 60)(x2, y2) --> (1, ?)(x3, y3) -->(0.982, 70)

5. Johnny measured the viscosity of his sample to be 1.55cP. What is the likely temperature of his sample?

(x1, y1) -->(1.794, 32)(x2, y2) -->(1.55, ?)(x3, y3) -->(1.546, 40)

6. What happens to water at 32oF? Do you expect that to affect the viscosity?

7. Use the data points at 180oF and 200oF to estimate the viscosity of water at 205oF. What is the danger of doing this?

(x1, y1) --> (180, 0.347)(x2, y2) --> (205, ?)(x3, y3) --> (200, 0.305)

8. Find the volume of steam at 550oF and 433psia.

(x1, y1) --> (400, 1.3840)(x2, y2) --> (433, ?)(x3, y3) --> (450, 1.2152)

Temperature, oF Pressure, 400psia Pressure, 450psia

550 1.3840 1.2152

9. Find the volume of steam at 600oF and 433psia.

(x1, y1) --> (400, 1.4765)(x2, y2) --> (433, ?)(x3, y3) --> (450, 1.3001)

Temperature, oF Pressure, 400psia Pressure, 450psia

600 1.4765 1.3001

10. Find the volume of steam at 571oF and 433psia.

(x1, y1) --> (550, 1.2726)(x2, y2) --> (571, ?)(x3, y3) --> (600, 1.3601)

Temperature, oF Pressure, 400psia Pressure, 433psia Pressure, 450psia

550 1.3840 1.2726 (from prob 8) 1.2152

600 1.4765 1.3601 (from prob 9) 1.3001

11. Find the volume of steam at 616oF and 630psia.

(x1, y1) --> (600, 0.94605)(x2, y2) --> (616, ?)(x3, y3) --> (650, 1.01133)

Temperature, oF Pressure, 600psia Pressure, 630psia Pressure, 700psia

600 0.94605 0.79332

616

650 1.01133 0.85242

(x1, y1) --> (600, 0.94605)(x2, y2) --> (630, ?)(x3, y3) --> (700, 0.79332)

OR

x = temperature x = pressure

11. Find the volume of steam at 616oF and 630psia.

(x1, y1) --> (600, 0.79332)(x2, y2) --> (616, ?)(x3, y3) --> (650, 0.85242)

Temperature, oF Pressure, 600psia Pressure, 630psia Pressure, 700psia

600 0.94605 0.79332

616 0.96694

650 1.01133 0.85242

11. Find the volume of steam at 616oF and 630psia.

(x1, y1) --> (600, 0.96694)(x2, y2) --> (630, ?)(x3, y3) --> (700, 0.81223)

Temperature, oF Pressure, 600psia Pressure, 630psia Pressure, 700psia

600 0.94605 0.79332

616 0.96694 0.81223

650 1.01133 0.85242

12. Find the volume of steam at 500oF and 616psia.

(x1, y1) --> (500, 0.99304)(x2, y2) --> (616, ?)(x3, y3) --> (600, 0.79526)

Temperature, oF Pressure, 500psia Pressure, 600psia

500 0.99304 0.79526