Question

the flow rate from a tap of diameter 1.25 cm is 3 l/min. the coefficient of viscosity of water is 10^-3 Pa s. Characterize the flow.​

Answer 1

ʟᴇᴛ ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ғʟᴏᴡ ʙᴇ ᴠ.

ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴛᴀᴘ = ᴅ = 1⃣.2⃣5⃣ ᴄᴍ = 1⃣.2⃣5⃣ ×1⃣0⃣-2⃣ ᴍ

ᴅᴇɴsɪᴛʏ ᴏғ ᴡᴀᴛᴇʀ = ρ = 1⃣0⃣3⃣ ᴋɢ ᴍ–3⃣

ᴠɪsᴄᴏsɪᴛʏ = η = 1⃣0⃣-3⃣ ᴘᴀ s

ᴛʜᴇ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ ᴡᴀᴛᴇʀ ғʟᴏᴡɪɴɢ ᴏᴜᴛ ᴘᴇʀ sᴇᴄᴏɴᴅ ɪs

ϙ = ᴠ × πᴅ2⃣/4⃣

ᴠ = 4⃣ϙ/ᴅ2⃣π

ᴛʜᴇ ʀᴇʏɴᴏʟᴅs ɴᴜᴍʙᴇʀ ɪs ɢɪᴠᴇɴ ʙʏ

ʀ = ρᴠᴅ/η

= 4⃣ρϙ/πᴅη

= 4⃣ ×1⃣0⃣3⃣ × ϙ/(3⃣.1⃣4⃣ × 1⃣.2⃣5⃣ ×1⃣0⃣-2⃣ × 1⃣0⃣-3⃣)

= 1⃣.0⃣1⃣9⃣ × 1⃣0⃣8⃣ ϙ

ɪɴɪᴛɪᴀʟʟʏ, ϙ = 0⃣.4⃣8⃣ ʟ / ᴍɪɴ = 0⃣.4⃣8⃣ × 1⃣0⃣-3⃣ / 6⃣0⃣ = 8⃣ × 1⃣0⃣-6⃣

ʀ = 8⃣1⃣5⃣

sɪɴᴄᴇ ᴛʜɪs ɪs ʙᴇʟᴏᴡ 1⃣0⃣0⃣0⃣, ᴛʜᴇ ғʟᴏᴡ ɪs sᴛᴇᴀᴅʏ.

ᴀғᴛᴇʀ sᴏᴍᴇ ᴛɪᴍᴇ, ϙ = 3⃣ ʟ / ᴍɪɴ = 3⃣ × 1⃣0⃣-3⃣ / 6⃣0⃣ = 5⃣ × 1⃣0⃣-5⃣

ʀ = 5⃣0⃣9⃣5⃣