This is a dual-program listing containing two independent BASIC programs. The first program (starting at line 10 with REM “HT”) is a heat transfer calculator that determines the convection coefficient for fluid flow through a circular pipe, implementing multiple correlations from standard heat transfer textbooks including the Hausen, Sieder-Tate, Dittus-Boelter, Colburn, and liquid-metal equations (8.51–8.60). It guides the user through laminar, turbulent, and entry-region flow regimes, computing the Reynolds number via RE=(4*M)/(PI*D*MU) and ultimately outputting H=K*NU/D. The second program (REM “A”) uses FAST/SLOW mode switching and computes a logarithmic curve over three nested ranges, printing W against a log-scale value using the log-10 conversion constant Z=0.4342944819 multiplied by 10*LN(0.25*W²+1).
Program Overview
The listing contains two completely independent programs. The first (lines 10–1650, labelled REM "HT") is an interactive heat transfer advisor. The second (lines 1–90, labelled REM "A") is a short mathematical table generator. They are presented in a single file but have no connection to each other.
Program 1 — “HT”: Structure
The program is organised as a decision tree that walks the user through the standard textbook procedure for calculating a pipe-flow convection coefficient H. The top-level branches are:
- Pipe geometry check (circular vs. non-circular) — lines 40–70
- Average (
B=1) or specific-location (B=2) value requested — lines 100–140 - Reynolds number calculation and laminar/turbulent split — lines 370–390
- Laminar sub-tree (fully developed / entry region) — lines 400–1060
- Turbulent sub-tree (small / large ΔT, liquid metals) — lines 1070–1605
- Final
Hcalculation and output — lines 1610–1640 - Out-of-range catch-all — line 1650
Program 1 — Key Equations Implemented
| Equation ref. | Correlation | BASIC line |
|---|---|---|
| Eq. 8.6 | RE = 4M / (π D μ) | 370 |
| Eq. 8.51 | NU = 4.36 (uniform flux, FD laminar) | 610 |
| Eq. 8.53 | NU = 3.66 (constant Ts, FD laminar) | 710 |
| Eq. 8.54 (Hausen) | NU = 3.66 + (0.0668·D·Re·Pr/L) / (1 + 0.04·(D·Re·Pr/L)^(2/3)) | 950 |
| Eq. 8.55 (Sieder-Tate laminar) | NU = 1.86·(Re·Pr/(L/D))^(1/3)·(μ/μs)^0.14 | 1030 |
| Eq. 8.57 (Colburn) | NU = 0.023·Re^0.8·Pr^(1/3) | 1260 |
| Eq. 8.58 (Dittus-Boelter) | NU = 0.023·Re^0.8·Pr^N (N=0.4 heating, 0.3 cooling) | 1340 |
| Eq. 8.59 (Sieder-Tate turbulent) | NU = 0.027·Re^0.8·Pr^(1/3)·(μ/μs)^0.14 | 1430 |
| Eq. 8.60 (liquid metal, const flux) | NU = 4.82 + 0.0185·Pe^0.827 | 1560 |
| — (liquid metal, const Ts) | NU = 5 + 0.025·Pe^0.8 | 1600 |
Program 1 — Notable Techniques and Idioms
- Input validation loops: Lines such as
60,130,590,690use the patternIF A<>1 AND A<>2 THEN GOTOto re-prompt on invalid input — a standard Sinclair-era idiom. - Re-use of
L: The variableLis first used as pipe length (line 90) and later reused at line 1300 as a heating/cooling flag (1 or 2). This shadows the original value and would give wrong results ifLwere needed afterwards — a latent bug since the Dittus-Boelter path (line 1350) goes straight to 1620 without needing the original length again, so it happens not to cause an error. - Reynolds number recalculated: Lines 928 and 1087 recalculate
REwith a new viscosity value (average mean temperature) before entering the Hausen and turbulent correlations respectively, correctly overwriting the earlier estimate. - Peclet number:
PE=RE*PR(line 1110) is computed once and reused for the liquid-metal correlations, avoiding redundant multiplication. - Dead code path for liquid metals: Line 1118 branches to line 1450 if
PRis in the liquid-metal range (0.003–0.05), but line 1450 itself begins withPRINT "LIQUID METAL"— this code is reachable only from line 1118, making it a separate functional block tucked after the turbulent main path. - Early exit via line 1650: Many validation checks simply jump to the single out-of-range message at line 1650 rather than implementing recovery, which keeps the program compact at the cost of user guidance.
- Line numbering gaps: Several intentional gaps (e.g. 95, 645, 845, 1055) were added later as patch-in lines, visible from the non-uniform numbering style.
Program 1 — Bugs and Anomalies
- Line 1360 is labelled
REM J=1 TEMP DIFF LARGEbut the condition at line 1230 isIF J=2 THEN GOTO 1360— so the large temperature difference path is actually taken whenJ=2(user answers “NO” to “small?”). The REM comment has the logic inverted. - The liquid-metal path (line 1460 onwards) is never reached from the turbulent tree for
B=2because line 1084 branches to 1090 (skipping line 1088), but line 1087 is only executed forB=1. This means for a specific-location turbulent liquid-metal case the Reynolds number is never updated to the mean-temperature value — a minor inconsistency. - Line 1345 is used as a
GOTOtarget from lines 1565 and 1605, but line 1345 readsPRINT "ENTER K (W/(M*K))"followed byINPUT Kat line 1347 and thenGOTO 1620at line 1350 — this works correctly but the jump destination mid-sequence is easy to misread.
Program 2 — “A”: Structure and Technique
This short program prints a table of W versus a log-scaled function of W over three progressively coarser ranges.
Z = 0.4342944819(line 2) is log₁₀(e), the natural-to-common-logarithm conversion factor. The expressionZ*10*LN(.25*W**2+1)therefore computes10·log₁₀(0.25W²+1).- The outer
FOR J=1 TO 3loop (line 10) selects three parameter pairs: range 0–1 step 0.1, range 0–10 step 1, range 0–100 step 10 — producing 11 rows each time. FAST/SLOWat lines 5 and 90 suppress display refresh during computation, a standard ZX81/TS1000 speed optimisation.- The branching logic at lines 20–42 uses a chain of
IF … GOTOto assignAandB, which is idiomatic for a platform withoutSELECT CASE.
Content
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Source Code
10 REM "HT"
20 PRINT "THIS PROGRAM CALCULATES THE CONVECTION COEFFICIENT FOR FLUID FLOW THROUGH A CIRCULAR PIPE"
30 PRINT
40 PRINT "IS THE PIPE CIRCULAR? (1 YES 2 NO)"
50 INPUT A
60 IF A<>1 AND A<>2 THEN GOTO 40
70 IF A=2 THEN GOTO 1650
80 PRINT "ENTER PIPE LENGTH (M)"
90 INPUT L
95 PRINT "PIPE LENGTH=";L;"M"
100 PRINT "IS AN AVERAGE (1) OR SPECIFIC (2) VALUE OF H REQUESTED?"
120 INPUT B
130 IF B<>1 AND B<>2 THEN GOTO 100
140 IF B=2 THEN GOTO 230
150 REM B=1 AVE H
160 PRINT "BASED ON THE DATA YOU HAVE, DECIDE ON A MEAN TEMP. FOR THE FLUID CONSIDERING THE ENTIRE PIPE"
190 PRINT "ENTER MEAN TEMP (K)"
200 INPUT C
210 PRINT "MEAN TEMP=";C;"K"
220 GOTO 270
230 REM B=2 SPEC H
240 PRINT "INPUT TEMP. AT DESIRED LOCATION (K)"
250 PRINT "IF NOT KNOWN EXACTLY, ENTER AN APPROX. VALUE"
255 INPUT T
260 PRINT "T=";T;"K"
270 REM CALC RE
280 PRINT "ENTER VISCOSITY AT TEMP. ABOVE (KG/(S*M))"
290 INPUT MU
300 PRINT "MU=";MU;" KG/(S*M)"
310 PRINT "ENTER FLOW RATE (KG/S)"
320 INPUT M
330 PRINT "M=";M;" KG/S"
340 PRINT "ENTER PIPE DIAMETER (M)"
350 INPUT D
360 PRINT "DIAMETER=";D;" M"
370 LET RE=(4*M)/(PI*D*MU)
380 PRINT "REYNOLDS NUMBER=";RE;" (EQ. 8.6)"
390 IF RE>=2300 THEN GOTO 1070
400 PRINT "FLOW IS LAMINAR"
410 LET XFD=.05*RE*D
420 PRINT "ENTRY LENGTH APPROX.=";XFD;" M"
430 IF B=1 THEN GOTO 470
440 PRINT "ENTER POINT OF INTEREST AS DISTANCE FROM INLET IN M"
450 INPUT X
460 GOTO 550
470 REM B=1 AVG VALUE
480 LET I=XFD/L
490 IF I>.05 THEN GOTO 530
500 PRINT "ENTRY REGION NOT SIGNIFICANT"
510 PRINT "USE AVERAGE VALUES FOR VARIABLES"
520 GOTO 560
530 PRINT "ENTRY REGION SIGNIFICANT"
540 GOTO 740
550 IF X<XFD THEN GOTO 740
560 PRINT "FLOW FULLY DEVELOPED"
570 PRINT "IS THERE UNIFORM HEAT FLUX? (1 YES 2 NO)"
580 INPUT E
590 IF E<>1 AND E<>2 THEN GOTO 570
600 IF E=2 THEN GOTO 660
610 LET NU=4.36
620 PRINT "EQ. 8.51 NUSSELT NO.=";NU
630 PRINT "ENTER VALUE OF K (W/(M*K)) AT MEAN TEMP"
640 INPUT K
645 PRINT "K=";K;"W/(M*K)"
650 GOTO 1620
660 REM E=2
670 PRINT "IS THE SURFACE TEMP. CONSTANT? (1 YES 2 NO)"
680 INPUT F
690 IF F<>1 AND F<>2 THEN GOTO 670
700 IF F=2 THEN GOTO 1650
710 LET NU=3.66
720 PRINT "EQ. 8.53 NUSSELT NO.=";NU
730 GOTO 630
740 PRINT "ENTRY REGION"
750 IF B=1 THEN GOTO 860
760 REM B=2 SPEC VALUE
770 PRINT "ENTER PRANDTL NO. AT POINT IN QUESTION"
780 INPUT PR
790 LET G=(X/D)/(RE*PR)
800 PRINT "REFER TO FIG. 8.8 TO DETERMINE NUSSELT NO. FOR (X/D)/(RE*PR)=";G
810 PRINT "ENTER NUSSELT NO."
820 INPUT NU
830 PRINT "ENTER K (W/(M*K)) AT POINT IN QUESTION"
840 INPUT K
845 PRINT "K=";K;"W/(M*K)"
850 GOTO 1610
860 REM B=1 AVG VALUE
870 PRINT "IS SURFACE TEMP. CONSTANT? (1 YES 2 NO)"
880 INPUT J
890 IF J<>1 AND J<>2 THEN GOTO 870
900 IF J=1 THEN GOTO 920
910 GOTO 1650
920 PRINT "ENTER ALL VALUES AT AVERAGE MEAN TEMP. (MEAN TEMP. IN+MEAN TEMP. OUT)/2"
925 PRINT "HAUSEN EQ. 8.54"
926 PRINT "ENTER AVG. VISCOSITY"
927 INPUT MU
928 LET RE=(4*M)/(PI*D*MU)
929 PRINT "NEW REYNOLDS NO.=";RE
930 PRINT "ENTER PRANDTL NO."
940 INPUT PR
950 LET NU=3.66+(.0668*D*RE*PR/L)/(1+.04*(D*RE*PR/L)**(2/3))
960 PRINT "NUSSELT NO.=";NU
970 PRINT "FOR IMPROVED ACCURACY: SIEDER-TATE EQ. 8.55"
980 IF PR<.48 OR PR>16700 THEN GOTO 1650
990 PRINT "ENTER VISCOSITY AT SURFACE TEMP"
\n1000 INPUT MUS
\n1010 PRINT "SURFACE VISCOSITY=";MUS;"KG/(S*M)"
\n1020 IF MU/MUS<.0044 OR MU/MUS>9.75 THEN GOTO 1650
\n1030 LET NU=1.86*(RE*PR/(L/D))**(1/3)*(MU/MUS)**.14
\n1040 PRINT "ENTER K (W/(M*K)) AT MEAN TEMP"
\n1050 INPUT K
\n1055 PRINT "K=";K;"W/(M*K)"
\n1060 GOTO 1610
\n1070 PRINT "FLOW IS TURBULENT"
\n1080 PRINT "IN THE ENTRY REGION THE RESULTS GIVEN WILL BE CRUDE APPROXIMATIONS"
\n1082 IF B=1 THEN PRINT "ENTER ALL VALUES AT AVG. MEAN TEMP."
\n1084 IF B=2 THEN GOTO 1090
\n1085 PRINT "ENTER AVG. VISCOSITY"
\n1086 INPUT MU
\n1087 LET RE=(4*M)/(PI*D*MU)
\n1088 PRINT "NEW REYNOLDS NO.=";RE
\n1090 PRINT "ENTER PRANDTL NO."
\n1100 INPUT PR
\n1105 PRINT "PR=";PR
\n1110 LET PE=RE*PR
\n1115 PRINT "PECLET NO. (PE)=";PE
\n1118 IF PR>=3E-3 AND PR<=5E-2 THEN GOTO 1450
\n1120 IF PR<.7 OR PR>160 THEN GOTO 1650
\n1130 IF RE<10000 THEN GOTO 1650
\n1140 IF (L/D)<60 THEN GOTO 1650
\n1200 PRINT "IS THE TEMP. DIFF. (SURFACE TEMP.-MEAN TEMP.) SMALL? (1 YES 2 NO)"
\n1210 INPUT J
\n1220 IF J<>1 AND J<>2 THEN GOTO 1200
\n1230 IF J=2 THEN GOTO 1360
\n1240 REM TEMP DIFF SMALL
\n1250 PRINT "COBURN EQ. 8.57"
\n1260 LET NU=.023*RE**.8*PR**(1/3)
\n1270 PRINT "NUSSELT NO.=";NU
\n1280 PRINT "PREFERRED: DITTUS-BOELTER EQ. 8.58"
\n1290 PRINT "IS HEATING (1) OR COOLING (2) TAKING PLACE?"
\n1300 INPUT L
\n1310 IF L<>1 AND L<>2 THEN GOTO 1290
\n1320 IF L=1 THEN LET N=.4
\n1330 IF L=2 THEN LET N=.3
\n1340 LET NU=.023*RE**.8*PR**N
\n1342 PRINT "NUSSELT NO.=";NU
\n1345 PRINT "ENTER K (W/(M*K))"
\n1347 INPUT K
\n1350 GOTO 1620
\n1360 REM J=1 TEMP DIFF LARGE
\n1370 IF PR<.7 OR PR>16700 THEN GOTO 1650
\n1380 IF RE<10000 OR (L/D)<60 THEN GOTO 1650
\n1400 PRINT "SIEDER/TATE EQ. 8.59"
\n1410 PRINT "ENTER SURFACE VISCOSITY (KG/(S*M))"
\n1420 INPUT MUS
\n1430 LET NU=.027*RE**.8*PR**(1/3)*(MU/MUS)**.14
\n1440 GOTO 1342
\n1460 PRINT "LIQUID METAL"
\n1480 PRINT "IS THE SURFACE HEAT FLUX CONSTANT (1), THE SURFACE TEMP. CONSTANT (2), OR NONE OF THE ABOVE?"
\n1490 INPUT Q
\n1500 IF Q<>1 AND Q<>2 AND Q<>3 THEN GOTO 1480
\n1510 IF Q=2 OR Q=3 THEN GOTO 1570
\n1520 REM HEAT FLUX CONST
\n1530 IF RE<3.6E3 OR RE>9.05E5 THEN GOTO 1650
\n1540 IF PE<100 OR PE>10000 THEN GOTO 1650
\n1550 PRINT "EQ. 8.60"
\n1560 LET NU=4.82+.0185*PE**.827
\n1565 GOTO 1345
\n1570 IF Q=3 THEN GOTO 1650
\n1580 REM Q=2 SURF TEMP CONST
\n1590 IF PE<=100 THEN GOTO 1650
\n1600 LET NU=5+.025*PE**.8
\n1605 GOTO 1345
\n1610 PRINT "NUSSELT NO.=";NU
\n1620 LET H=(K*NU)/D
\n1630 PRINT "HEAT TRANSFER COEFFICIENT=";H;"W/(M**2*K)"
\n1640 STOP
\n1650 PRINT "OUT OF RANGE OF PROGRAM, CONSULT LITERATURE"
1 REM "A"
2 LET Z=.4342944819
5 FAST
10 FOR J=1 TO 3
20 IF J=2 OR J=3 THEN GOTO 30
22 LET A=1
24 LET B=.1
26 GOTO 50
30 IF J=3 THEN GOTO 40
32 LET A=10
34 LET B=1
36 GOTO 50
40 LET A=100
42 LET B=10
50 FOR W=0 TO A STEP B
60 LET X=Z*10*LN (.25*W**2+1)
70 PRINT W,X
80 NEXT W
85 NEXT J
90 SLOW
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