{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmmu-pro","formal_name":"MMMU-Pro","introduction":"MMMU-Pro evaluates multimodal understanding across academic disciplines using images and text. The official card lists 1,730 questions per setting, separating four-option and ten-option standard settings from the vision setting.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://mmmu-benchmark.github.io/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"f6ccd02e-a6f0-5d00-9874-3217700a29bf","task_key":"standard~20~2810~20options~29--test--validation~5fEnergy~5fand~5fPower~5f28","task_revision_id":"3","upstream_id":"validation_Energy_and_Power_28","short_description":"A pipe of radius R has a fully developed laminarflow of air at P0, T0 with a…","config":"standard (10 options)","split":"test","body":"{\"img_type\":\"['Diagrams']\",\"options\":\"['$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{2}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{3\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{4}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{2}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{4}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^4\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{2}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{5}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{2}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{4\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{3}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$', '$\\\\\\\\begin{aligned}V&=\\\\\\\\frac{V_c}{3}\\\\\\\\\\\\\\\\\\\\\\\\dot{m}&=\\\\\\\\frac{\\\\\\\\pi}{2\\\\\\\\cdot\\\\\\\\nu}\\\\\\\\cdot V_c\\\\\\\\cdot R^2\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\end{aligned}$']\",\"question\":\"A pipe of radius R has a fully developed laminarflow of air at P0, T0 with a velocity profile of V = Vc[1 - (r/R)2], where Vc is the velocity on the center-line and r is the radius, as shown in <image 1>. Find the total mass flow rate and the average velocity, both as functions of Vc and R.\",\"subject\":\"Energy_and_Power\"}","display_format":"text","language":"","answer_status":"published","assets":[{"kind":"file","reference_id":"task:f6ccd02e-a6f0-5d00-9874-3217700a29bf:3:image_1.png","filename":"image_1.png","media_type":"image/png","alt":""}],"source_url":"https://mmmu-benchmark.github.io/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}